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  • 1. Aaghabali, M.
    et al.
    Akbari, S.
    Friedland, S.
    Markström, Klas
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Tajfirouz, Z.
    Upper bounds on the number of perfect matchings and directed 2-factors in graphs with given number of vertices and edges2015In: European journal of combinatorics (Print), ISSN 0195-6698, E-ISSN 1095-9971, Vol. 45, 132-144 p.Article in journal (Refereed)
    Abstract [en]

    We give an upper bound on the number of perfect matchings in simple graphs with a given number of vertices and edges. We apply this result to give an upper bound on the number of 2-factors in a directed complete bipartite balanced graph on 2n vertices. The upper bound is sharp for even n. For odd n we state a conjecture on a sharp upper bound.

  • 2. Adamaszek, Michal
    et al.
    Barmak, Jonathan Ariel
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    On a lower bound for the connectivity of the independence complex of a graph2011In: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 311, no 21, 2566-2569 p.Article in journal (Refereed)
    Abstract [en]

    Aharoni, Berger and Ziv proposed a function which is a lower bound for the connectivity of the independence complex of a graph. They conjectured that this bound is optimal for every graph. We give two different arguments which show that the conjecture is false.

  • 3.
    Ahmad, Naseer
    Blekinge Institute of Technology, School of Engineering, Department of Telecommunication Systems.
    Security Issues in Wireless Systems2009Independent thesis Advanced level (degree of Master (One Year))Student thesis
    Abstract [en]

    ireless Communication is one of the fields of Telecommunications which is growing with the tremendous speed. With the passage of time wireless communication devices are becoming more and more common. It is not only the technology of business but now people are using it to perform their daily tasks, be it for calling, shopping, checking their emails or transfer their money. Wireless communication devices include cellular phones, cordless phones and satellite phones, smart phones like Personal Digital Assistants (PDA), two way pagers, and lots of their devices are on their way to improve this wireless world. In order to establish two way communications, a wireless link may be using radio waves or Infrared light. The Wireless communication technologies have become increasingly popular in our everyday life. The hand held devices like Personal Digital Assistants (PDA) allow the users to access calendars, mails, addresses, phone number lists and the internet. Personal digital assistants (PDA) and smart phones can store large amounts of data and connect to a broad spectrum of networks, making them as important and sensitive computing platforms as laptop PCs when it comes to an organization’s security plan. Today’s mobile devices offer many benefits to enterprises. Mobile phones, hand held computers and other wireless systems are becoming a tempting target for virus writers. Mobile devices are the new frontier for viruses, spam and other potential security threats. Most viruses, Trojans and worms have already been created that exploit vulnerabilities. With an increasing amount of information being sent through wireless channels, new threats are opening up. Viruses have been growing fast as handsets increasingly resemble small computers that connect with each other and the internet. Hackers have also discovered that many corporate wireless local area networks (WLAN) in major cities were not properly secured. Mobile phone operators say that it is only a matter of time before the wireless world is hit by the same sorts of viruses and worms that attack computer software.

  • 4.
    Andren, Daniel
    et al.
    Umeå University.
    Hellström, Lars
    Umeå University.
    Markström, Klas
    Umeå University.
    Fast multiplication of matrices over a finitely generated semiring2008In: Information Processing Letters, ISSN 0020-0190, E-ISSN 1872-6119, Vol. 107, no 6, 230-234 p.Article in journal (Refereed)
  • 5.
    Andren, Lina J.
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Casselgren, Carl Johan
    Öhman, Lars-Daniel
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Avoiding Arrays of Odd Order by Latin Squares2013In: Combinatorics, probability & computing, ISSN 0963-5483, E-ISSN 1469-2163, Vol. 22, no 2, 184-212 p.Article in journal (Refereed)
    Abstract [en]

    We prove that there is a constant c such that, for each positive integer k, every (2k + 1) x (2k + 1) array A on the symbols 1, ... , 2k + 1 with at most c(2k + 1) symbols in every cell, and each symbol repeated at most c(2k + 1) times in every row and column is avoidable; that is, there is a (2k + 1) x (2k + 1) Latin square S on the symbols 1, ... , 2k + 1 such that, for each i, j is an element of {1, ... , 2k + 1}, the symbol in position (i, j) of S does not appear in the corresponding cell in Lambda. This settles the last open case of a conjecture by Haggkvist. Using this result, we also show that there is a constant rho, such that, for any positive integer n, if each cell in an n x n array B is assigned a set of m <= rho n symbols, where each set is chosen independently and uniformly at random from {1, ... , n}, then the probability that B is avoidable tends to 1 as n -> infinity.

  • 6.
    Andrén, Daniel
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    On the Ising problem and some matrix operations2007Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    The first part of the dissertation concerns the Ising problem proposed to Ernst Ising by his supervisor Wilhelm Lenz in the early 20s. The Ising model, or perhaps more correctly the Lenz-Ising model, tries to capture the behaviour of phase transitions, i.e. how local rules of engagement can produce large scale behaviour.

    Two decades later Lars Onsager solved the Ising problem for the quadratic lattice without an outer field. Using his ideas solutions for other lattices in two dimensions have been constructed. We describe a method for calculating the Ising partition function for immense square grids, up to linear order 320 (i.e. 102400 vertices).

    In three dimensions however only a few results are known. One of the most important unanswered questions is at which temperature the Ising model has its phase transition. In this dissertation it is shown that an upper bound for the critical coupling Kc, the inverse absolute temperature, is 0.29 for the tree dimensional cubic lattice.

    To be able to get more information one has to use different statistical methods. We describe one sampling method that can use simple state generation like the Metropolis algorithm for large lattices. We also discuss how to reconstruct the entropy from the model, in order to obtain parameters as the free energy.

    The Ising model gives a partition function associated with all finite graphs. In this dissertation we show that a number of interesting graph invariants can be calculated from the coefficients of the Ising partition function. We also give some interesting observations about the partition function in general and show that there are, for any N, N non-isomorphic graphs with the same Ising partition function.

    The second part of the dissertation is about matrix operations. We consider the problem of multiplying them when the entries are elements in a finite semiring or in an additively finitely generated semiring. We describe a method that uses O(n3 / log n) arithmetic operations.

    We also consider the problem of reducing n x n matrices over a finite field of size q using O(n2 / logq n) row operations in the worst case.

  • 7.
    Andrén, Lina J.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Avoidability of random arraysManuscript (preprint) (Other academic)
    Abstract [en]

    An n×n array that in each cell contains a subset of the symbols 1, . . . , n is avoidable if there exists a Latin square of order n such that no cell in the Latin square contains a symbol which belongs to the set of symbols in the corresponding cell of the array. Some results on deterministic conditions for avoidability of arrays have been found, but here we study the problem of having an array with randomly assigned subsets of C in its cells. This is equivalent to the problem of list-edge-coloring  with randomly assigned lists from the set {1, . . . , n}. We show that an array where each symbol appears in each cell with probability p will be avoidable with very high probability even if p is such that the expected number of symbols forbidden in each cell is slightly higher than what deterministic theorems can prove is avoidable.

  • 8.
    Andrén, Lina J.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Avoiding (m, m, m)-arrays of order n = 2kManuscript (preprint) (Other academic)
    Abstract [en]

    An (m, m, m)-array of order n is an n × n array such that each cell is assigned a set of at most m symbols from {1,...,n} such that no symbol occurs more than m times in any row or column. An (m,m,m)- array is called avoidable if there exists a Latin square such that no cell in the Latin square contains a symbol that also belongs to the set assigned to the corresponding cell in the array. We show that there is a constant γ such that if m ≤ γ2k, then any (m,m,m)-array of order 2k is avoidable. Such a constant γ has been conjectured to exist for all n by Häggkvist.

  • 9.
    Andrén, Lina J.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Avoidability by Latin squares of arrays of even orderManuscript (preprint) (Other academic)
    Abstract [en]

    We prove that for any k and any 2k × 2k array A such that no cell in A contains more than   k/2550 symbols, and no symbol occurs more than k/2550 times in any row or column, there is a Latin square such that no 2550cell in the Latin square contains a symbol that occurs in the corresponding cell in A. This proves a conjecture of Häggkvist [8] in the special case of arrays with even side.

  • 10.
    Andrén, Lina J.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    On Latin squares and avoidable arrays2010Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis consists of the four papers listed below and a survey of the research area.

    I Lina J. Andrén: Avoiding (m, m, m)-arrays of order n = 2k

    II Lina J. Andrén: Avoidability of random arrays

    III Lina J. Andr´en: Avoidability by Latin squares of arrays with even order

    IV Lina J. Andrén, Carl Johan Casselgren and Lars-Daniel Öhman: Avoiding arrays of odd order by Latin squares

    Papers I, III and IV are all concerned with a conjecture by Häggkvist saying that there is a constant c such that for any positive integer n, if m ≤ cn, then for every n × n array A of subsets of {1, . . . , n} such that no cell contains a set of size greater than m, and none of the elements 1, . . . , n belongs to more than m of the sets in any row or any column of A, there is a Latin square L on the symbols 1, . . . , n such that there is no cell in L that contains a symbol that belongs to the set in the corresponding cell of A. Such a Latin square is said to avoid A. In Paper I, the conjecture is proved in the special case of order n = 2k . Paper III improves on the techniques of Paper I, expanding the proof to cover all arrays of even order. Finally, in Paper IV, similar methods are used together with a recoloring theorem to prove the conjecture for all orders. Paper II considers another aspect of the problem by asking to what extent way a deterministic result concerning the existence of Latin squares that avoid certain arrays can be used when the sets in the array are assigned randomly.

  • 11.
    Andrén, Lina J.
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Casselgren, Carl Johan
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Öhman, Lars-Daniel
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Avoiding arrays of odd order by Latin squaresManuscript (preprint) (Other academic)
    Abstract [en]

    We prove that there exists a constant c such that for each pos- itive integer k every (2k+1)×(2k+1) array A on the symbols 1,...,2k+1 with at most c(2k + 1) symbols in every cell, and each symbol repeated at most c(2k+1) times in every row and column is avoidable; that is, there is a (2k+1)×(2k+1) Latin square S on the symbols 1,...,2k+1 such that for each cell (i, j) in S the symbol in (i, j) does not appear in the corresponding cell in A. This settles the last open case of a conjecture by Häggkvist.

  • 12.
    Arkin, Esther M
    et al.
    Department of Applied Mathematics and Statistics, Stony Brook University, USA .
    Dieckmann, Claudia
    Institute of Computer Science, Freie Universität Berlin, Germany .
    Knauer, Christian
    Institute of Computer Science, Universität Bayreuth, Germany .
    Mitchell, Joseph SB
    Department of Applied Mathematics and Statistics, Stony Brook University, USA .
    Polishchuk, Valentin
    Helsinki Institute for Information Technology, CS Dept, University of Helsinki, Finland .
    Schlipf, Lena
    Institute of Computer Science, Freie Universität Berlin, Germany .
    Yang, Shang
    Department of Computer Science, Stony Brook University, USA .
    Convex transversals2014In: Computational Geometry, ISSN 0925-7721, Vol. 47, no 2, 224-239 p.Article in journal (Refereed)
    Abstract [en]

    We answer the question initially posed by Arik Tamir at the Fourth NYU Computational Geometry Day (March, 1987): “Given a collection of compact sets, can one decide in polynomial time whether there exists a convex body whose boundary intersects every set in the collection?”

    We prove that when the sets are segments in the plane, deciding existence of the convex stabber is NP-hard. The problem remains NP-hard if the sets are regular polygons. We also show that in 3D the stabbing problem is hard when the sets are balls. On the positive side, we give a polynomial-time algorithm to find a convex transversal of a maximum number of pairwise-disjoint segments in 2D if the vertices of the transversal are restricted to a given set of points. Our algorithm also finds a convex stabber of the maximum number of a set of convex pseudodisks in the plane.

    The stabbing problem is related to “convexity” of point sets measured as the minimum distance by which the points must be shifted in order to arrive in convex position; we give a PTAS to find the minimum shift in 2D, and a 2-approximation in any dimension. We also consider stabbing with vertices of a regular polygon – a problem closely related to approximate symmetry detection.

  • 13.
    Asratian, Armen
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Casselgren, Carl Johan
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering. University of Southern Denmark, Denmark.
    Solution of Vizings Problem on Interchanges for the case of Graphs with Maximum Degree 4 and Related Results2016In: Journal of Graph Theory, ISSN 0364-9024, E-ISSN 1097-0118, Vol. 82, no 4, 350-373 p.Article in journal (Refereed)
    Abstract [en]

    Let G be a Class 1 graph with maximum degree 4 and let t amp;gt;= 5 be an integer. We show that any proper t-edge coloring of G can be transformed to any proper 4-edge coloring of G using only transformations on 2-colored subgraphs (so-called interchanges). This settles the smallest previously unsolved case of a well-known problem of Vizing on interchanges, posed in 1965. Using our result we give an affirmative answer to a question of Mohar for two classes of graphs: we show that all proper 5-edge colorings of a Class 1 graph with maximum degree 4 are Kempe equivalent, that is, can be transformed to each other by interchanges, and that all proper 7-edge colorings of a Class 2 graph with maximum degree 5 are Kempe equivalent. (C) 2015 Wiley Periodicals, Inc.

  • 14.
    Asratian, Armen S.
    et al.
    Linköping University, Linköping, Sweden.
    Casselgren, Carl Johan
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Vandenbussche, Jennifer
    Southern Polytechnic State University, Marietta, Georgia.
    West, Douglas B.
    University of Illinois, Urbana, Illinois.
    Proper path-factors and interval edge-coloring of (3,4)-biregular bigraphs2009In: Journal of Graph Theory, ISSN 0364-9024, E-ISSN 1097-0118, Vol. 61, no 2, 88-97 p.Article in journal (Refereed)
    Abstract [en]

    An interval coloring of a graph G is a proper coloring of E(G) by positive integers such that the colors on the edges incident to any vertex are consecutive. A (3,4)-biregular bigraph is a bipartite graph in which each vertex of one part has degree 3 and each vertex of the other has degree 4; it is unknown whether these all have interval colorings. We prove that G has an interval coloring using 6 colors when G is a (3,4)-biregular bigraph having a spanning subgraph whose components are paths with endpoints at 3-valent vertices and lengths in {2, 4, 6, 8}. We provide several sufficient conditions for the existence of such a subgraph.

  • 15.
    Austrin, Per
    et al.
    KTH, School of Computer Science and Communication (CSC), Theoretical Computer Science, TCS.
    Benabbas, Siavosh
    Georgiou, Konstantinos
    Better Balance by Being Biased: A 0.8776-Approximation for Max Bisection2016In: ACM Transactions on Algorithms, ISSN 1549-6325, E-ISSN 1549-6333, Vol. 13, no 1, 2Article in journal (Refereed)
    Abstract [en]

    Recently, Raghavendra and Tan (SODA 2012) gave a 0.85-approximation algorithm for the MAX BISECTION problem. We improve their algorithm to a 0.8776-approximation. As MAX BISECTION is hard to approximate within alpha(GW) + epsilon approximate to 0.8786 under the Unique Games Conjecture (UGC), our algorithm is nearly optimal. We conjecture that MAX BISECTION is approximable within alpha(GW) - epsilon, that is, that the bisection constraint (essentially) does not make MAX CUT harder. We also obtain an optimal algorithm (assuming the UGC) for the analogous variant of MAX 2-SAT. Our approximation ratio for this problem exactly matches the optimal approximation ratio for MAX 2-SAT, that is, alpha(LLZ) + epsilon approximate to 0.9401, showing that the bisection constraint does not make MAX 2-SAT harder. This improves on a 0.93-approximation for this problem from Raghavendra and Tan.

  • 16.
    Austrin, Per
    et al.
    KTH, School of Computer Science and Communication (CSC), Theoretical Computer Science, TCS.
    Kaski, P.
    Koivisto, M.
    Nederlöf, J.
    Dense Subset Sum may be the hardest2016In: Leibniz International Proceedings in Informatics, LIPIcs, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing , 2016Conference paper (Refereed)
    Abstract [en]

    The Subset Sum problem asks whether a given set of n positive integers contains a subset of elements that sum up to a given target t. It is an outstanding open question whether the O∗(2n/2)-time algorithm for Subset Sum by Horowitz and Sahni [J. ACM 1974] can be beaten in the worst-case setting by a "truly faster", O∗(2(0.5-δ)n)-time algorithm, with some constant δ &gt; 0. Continuing an earlier work [STACS 2015], we study Subset Sum parameterized by the maximum bin size β, defined as the largest number of subsets of the n input integers that yield the same sum. For every ∈ &gt; 0 we give a truly faster algorithm for instances with β ≤ 2(0.5-∈)n, as well as instances with β ≥ 20.661n. Consequently, we also obtain a characterization in terms of the popular density parameter n/log2 t: if all instances of density at least 1.003 admit a truly faster algorithm, then so does every instance. This goes against the current intuition that instances of density 1 are the hardest, and therefore is a step toward answering the open question in the affirmative. Our results stem from a novel combinatorial analysis of mixings of earlier algorithms for Subset Sum and a study of an extremal question in additive combinatorics connected to the problem of Uniquely Decodable Code Pairs in information theory.

  • 17. Averkov, Gennadiy
    et al.
    Krümpelmann, Jan
    Nill, Benjamin
    Stockholm University, Faculty of Science, Department of Mathematics.
    Largest integral simplices with one interior integral point: Solution of Hensley's conjecture and related results2015In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 274, 118-166 p.Article in journal (Refereed)
    Abstract [en]

    For each dimension d, d-dimensional integral simplices with exactly one interior integral point have bounded volume. This was first shown by Hensley. Explicit volume bounds were determined by Hensley, Lagarias and Ziegler, Pikhurko, and Averkov. In this paper we determine the exact upper volume bound for such simplices and characterize the volume-maximizing simplices. We also determine the sharp upper bound on the coefficient of asymmetry of an integral polytope with a single interior integral point. This result confirms a conjecture of Hensley from 1983. Moreover, for an integral simplex with precisely one interior integral point, we give bounds on the volumes of its faces, the barycentric coordinates of the interior integral point and its number of integral points. Furthermore, we prove a bound on the lattice diameter of integral polytopes with a fixed number of interior integral points. The presented results have applications in toric geometry and in integer optimization.

  • 18.
    Ball, Simeon
    et al.
    Universitat Politècnica de Catalunya, Barcelona, Spain.
    Bamberg, John
    The University of Western Australia, Crawley, WA, Australia.
    Devillers, Alice
    The University of Western Australia, Crawley, WA, Australia.
    Stokes, Klara
    Universitat Rovira i Virgili, Tarragona, Spain.
    An alternative way to generalise the pentagon2013In: Journal of combinatorial designs (Print), ISSN 1063-8539, E-ISSN 1520-6610, Vol. 21, no 4, 163-179 p.Article in journal (Refereed)
    Abstract [en]

    We introduce the concept of a pentagonal geometry as a generalization of the pentagon and the Desargues configuration, in the same vein that the generalized polygons share the fundamental properties of ordinary polygons. In short, a pentagonal geometry is a regular partial linear space in which for all points x, the points not collinear with the point x, form a line. We compute bounds on their parameters, give some constructions, obtain some nonexistence results for seemingly feasible parameters and suggest a cryptographic application related to identifying codes of partial linear spaces.

  • 19.
    Balletti, Gabriele
    Stockholm University, Faculty of Science, Department of Mathematics.
    Classifications and volume bounds of lattice polytopes2017Licentiate thesis, monograph (Other academic)
    Abstract [en]

    In this licentiate thesis we study relations among invariants of lattice polytopes, with particular focus on bounds for the volume.In the first paper we give an upper bound on the volume vol(P^*) of a polytope P^* dual to a d-dimensional lattice polytope P with exactly one interiorlattice point, in each dimension d. This bound, expressed in terms of the Sylvester sequence, is sharp, and is achieved by the dual to a particular reflexive simplex. Our result implies a sharp upper bound on the volume of a d-dimensional reflexive polytope. In the second paper we classify the three-dimensional lattice polytopes with two lattice points in their strict interior. Up to unimodular equivalence thereare 22,673,449 such polytopes. This classification allows us to verify, for this case only, the sharp conjectural upper bound for the volume of a lattice polytope with interior points, and provides strong evidence for more general new inequalities on the coefficients of the h^*-polynomial in dimension three.

  • 20.
    Baltz, Andreas
    et al.
    Christian-Albrechts Universität Kiel.
    El Ouali, Mourad
    Christian-Albrechts Universität Kiel.
    Jäger, Gerold
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Sauerland, Volkmar
    Christian-Albrechts Universität Kiel.
    Srivastav, Anand
    Christian-Albrechts Universität Kiel.
    Exact and heuristic algorithms for the Travelling Salesman Problem with Multiple Time Windows and Hotel Selection2015In: Journal of the Operational Research Society, ISSN 0160-5682, E-ISSN 1476-9360, Vol. 66, no 4, 615-626 p.Article in journal (Refereed)
    Abstract [en]

    We introduce and study the Travelling Salesman Problem with Multiple Time Windows and Hotel Selection (TSP-MTWHS), which generalises the well-known Travelling Salesman Problem with Time Windows and the recently introduced Travelling Salesman Problem with Hotel Selection. The TSP-MTWHS consists in determining a route for a salesman (eg, an employee of a services company) who visits various customers at different locations and different time windows. The salesman may require a several-day tour during which he may need to stay in hotels. The goal is to minimise the tour costs consisting of wage, hotel costs, travelling expenses and penalty fees for possibly omitted customers. We present a mixed integer linear programming (MILP) model for this practical problem and a heuristic combining cheapest insert, 2-OPT and randomised restarting. We show on random instances and on real world instances from industry that the MILP model can be solved to optimality in reasonable time with a standard MILP solver for several small instances. We also show that the heuristic gives the same solutions for most of the small instances, and is also fast, efficient and practical for large instances.

  • 21.
    Baltz, Andreas
    et al.
    Christian-Albrechts-Universität Kiel, Germany.
    Jäger, Gerold
    Christian-Albrechts-Universität Kiel, Germany.
    Srivastav, Anand
    Christian-Albrechts-Universität Kiel, Germany.
    Constructions of Sparse Asymmetric Connectors2003In: Proceedings of 23rd Conference of Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2003) / [ed] P.K. Lodaya and J. Radhakrishnan, Berlin-Heidelberg: Springer Berlin/Heidelberg, 2003, 13-22 p.Conference paper (Refereed)
  • 22.
    Baltz, Andreas
    et al.
    Christian-Albrechts Universität Kiel, Germany.
    Jäger, Gerold
    Christian-Albrechts Universität Kiel, Germany.
    Srivastav, Anand
    Christian-Albrechts Universität Kiel, Germany.
    Construction of Sparse Asymmetric Connectors2003In: Proceedings of European Conference on Combinatorics, Graph Theory and Applications (Eurocomb 2003), 2003Conference paper (Refereed)
  • 23.
    Baltz, Andreas
    et al.
    Mathematisches seminar, Christian-Albrechts-Universität zu Kiel, Germany.
    Jäger, Gerold
    Mathematisches seminar, Christian-Albrechts-Universität zu Kiel, Germany.
    Srivastav, Anand
    Mathematisches seminar, Christian-Albrechts-Universität zu Kiel, Germany.
    Constructions of Sparse Asymmetric Connectors with Number Theoretic Methods2005In: Networks, ISSN 0028-3045, E-ISSN 1097-0037, Vol. 45, no 3, 119-124 p.Article in journal (Refereed)
    Abstract [en]

    We consider the problem of connecting a set I of n inputs to a set O of N outputs (n ≤ N) by as few edges as possible such that for every injective mapping f : I → O there are n vertex disjoint paths from i to f(i) of length k for a given k . For k = Ω(log N + logn) Oruς (1994) gave the presently best (n,N)-connector with O(N+n·log n) edges. For k=2 and N the square of a prime, Richards and Hwang (1985) described a construction using edges. We show by a probabilistic argument that an optimal (n,N)-connector has Θ (N) edges, if for some ε>0. Moreover, we give explicit constructions based on a new number theoretic approach that need at most edges for arbitrary choices of n and N. The improvement we achieve is based on applying a generalization of the Erdös-Heilbronn conjecture on the size of restricted sums.

  • 24. Barak, B.
    et al.
    Gopalan, P.
    Håstad, Johan
    KTH, School of Computer Science and Communication (CSC), Theoretical Computer Science, TCS.
    Meka, R.
    Raghavendra, P.
    Steurer, D.
    Making the long code shorter2015In: SIAM journal on computing (Print), ISSN 0097-5397, E-ISSN 1095-7111, Vol. 44, no 5, 1287-1324 p.Article in journal (Refereed)
    Abstract [en]

    The long code is a central tool in hardness of approximation especially in questions related to the Unique Games Conjecture. We construct a new code that is exponentially more efficient but can still be used in many of these applications. Using the new code we obtain exponential improvements over several known results including the following: (1) For any ε &gt; 0, we show the existence of an n-vertex graph G where every set of o(n) vertices has expansion 1-ε but G's adjacency matrix has more than exp(logδ n) eigenvalues larger than 1 - ε, where δ depends only on ε. This answers an open question of Arora, Barak, and Steurer [Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, 2010, pp. 563-572] who asked whether one can improve over the noise graph on the Boolean hypercube that has poly(log n) such eigenvalues. (2) A gadget that reduces Unique Games instances with linear constraints modulo K into instances with alphabet k with a blowup of kpolylog(K) , improving over the previously known gadget with blowup of kω(K). (3) An n-variable integrality gap for Unique Games that survives exp(poly(log log n)) rounds of the semidefinite programming version of the Sherali-Adams hierarchy, improving on the previously known bound of poly(log log n). We show a connection between the local testability of linear codes and Small-Set Expansion in certain related Cayley graphs and use this connection to derandomize the noise graph on the Boolean hypercube.

  • 25.
    Belova, Anna
    et al.
    Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE).
    Shmidt, Tamara
    Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), MPE-lab.
    Meshfree methods in option pricing2011Independent thesis Advanced level (degree of Master (One Year)), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    A meshfree approximation scheme based on the radial basis function methods is presented for the numerical solution of the options pricing model. This thesis deals with the valuation of the European, Barrier, Asian, American options of a single asset and American options of multi assets. The option prices are modeled by the Black-Scholes equation. The θ-method is used to discretize the equation with respect to time. By the next step, the option price is approximated in space with radial basis functions (RBF) with unknown parameters, in particular, we con- sider multiquadric radial basis functions (MQ-RBF). In case of Ameri- can options a penalty method is used, i.e. removing the free boundary is achieved by adding a small and continuous penalty term to the Black- Scholes equation. Finally, a comparison of analytical and finite difference solutions and numerical results from the literature is included.

  • 26.
    Berglund, Alexander
    Stockholm University, Faculty of Science, Department of Mathematics.
    Shellability and the strong gcd-condition2009In: The Electronic Journal of Combinatorics, ISSN 1077-8926, Vol. 16, no 2Article in journal (Refereed)
    Abstract [en]

    Shellability is a well-known combinatorial criterion on a simplicial complex for verifying that the associated Stanley-Reisner ring k[] is Cohen-Macaulay. Anotion familiar to commutative algebraists, but which has not received as muchattention from combinatorialists as the Cohen-Macaulay property, is the notion ofa Golod ring. Recently, J¨ollenbeck introduced a criterion on simplicial complexesreminiscent of shellability, called the strong gcd-condition, and he together with theauthor proved that it implies Golodness of the associated Stanley-Reisner ring. Thetwo algebraic notions were earlier tied together by Herzog, Reiner and Welker, whoshowed that if k[∨] is sequentially Cohen-Macaulay, where ∨ is the Alexanderdual of , then k[] is Golod. In this paper, we present a combinatorial companionof this result, namely that if ∨ is (non-pure) shellable then satisfies the stronggcd-condition. Moreover, we show that all implications just mentioned are strict ingeneral but that they are equivalences if is a flag complex.

  • 27.
    Berglund, Alexander
    Stockholm University, Faculty of Science, Department of Mathematics.
    Shellability and the strong gcd-condition2009In: The Electronic Journal of Combinatorics, ISSN 1077-8926, Vol. 16, no 2Article in journal (Refereed)
    Abstract [en]

    Shellability is a well-known combinatorial criterion on a simplicial complex for verifying that the associated Stanley-Reisner ring k[] is Cohen-Macaulay. Anotion familiar to commutative algebraists, but which has not received as muchattention from combinatorialists as the Cohen-Macaulay property, is the notion ofa Golod ring. Recently, J¨ollenbeck introduced a criterion on simplicial complexesreminiscent of shellability, called the strong gcd-condition, and he together with theauthor proved that it implies Golodness of the associated Stanley-Reisner ring. Thetwo algebraic notions were earlier tied together by Herzog, Reiner and Welker, whoshowed that if k[∨] is sequentially Cohen-Macaulay, where ∨ is the Alexanderdual of , then k[] is Golod. In this paper, we present a combinatorial companionof this result, namely that if ∨ is (non-pure) shellable then satisfies the stronggcd-condition. Moreover, we show that all implications just mentioned are strict ingeneral but that they are equivalences if is a flag complex.

  • 28. Bhattacharya, S.
    et al.
    Henzinger, M.
    Na Nongkai, Danupon
    KTH, School of Computer Science and Communication (CSC), Theoretical Computer Science, TCS.
    New deterministic approximation algorithms for fully dynamic matching2016Conference paper (Refereed)
    Abstract [en]

    We present two deterministic dynamic algorithms for the maximum matching problem. (1) An algorithm that maintains a (2 + ϵ)-approximate maximum matching in general graphs with O(poly(log n, 1/ϵ)) update time. (2) An algorithm that maintains an αk approximation of the value of the maximum matching with O(n2/K) update time in bipartite graphs, for every sufficiently large constant positive integer K. Here, 1 ≤ αk ≤ 2 is a constant determined by the value of K. Result (1) is the first deterministic algorithm that can maintain an o(log n)-approximate maximum matching with polylogarithmic update time, improving the seminal result of Onak et al. [STOC 2010]. Its approximation guarantee almost matches the guarantee of the best randomized polylogarithmic update time algorithm [Baswana et al. FOCS 2011]. Result (2) achieves a better-than-two approximation with arbitrarily small polynomial update time on bipartite graphs. Previously the best update time for this problem was O(m1/4) [Bernstein et al. ICALP 2015], where m is the current number of edges in the graph.

  • 29. Bierbrauer, Jürgen
    et al.
    Schellwat, Holger
    Örebro University, Department of Natural Sciences.
    Almost independent and weakly biased arrays: efficient constructions and cryptologic applications2000In: Advances in cryptology: CRYPTO 2000 / [ed] Mihir Bellare, Springer Berlin/Heidelberg, 2000, 533-543 p.Conference paper (Other academic)
  • 30.
    Björnberg, Jakob Erik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Graphical representations of Ising and Potts models: Stochastic geometry of the quantum Ising model and the space-time Potts model2009Doctoral thesis, monograph (Other academic)
    Abstract [en]

    HTML clipboard Statistical physics seeks to explain macroscopic properties of matter in terms of microscopic interactions. Of particular interest is the phenomenon of phase transition: the sudden changes in macroscopic properties as external conditions are varied. Two models in particular are of great interest to mathematicians, namely the Ising model of a magnet and the percolation model of a porous solid. These models in turn are part of the unifying framework of the random-cluster representation, a model for random graphs which was first studied by Fortuin and Kasteleyn in the 1970’s. The random-cluster representation has proved extremely useful in proving important facts about the Ising model and similar models.

    In this work we study the corresponding graphical framework for two related models. The first model is the transverse field quantum Ising model, an extension of the original Ising model which was introduced by Lieb, Schultz and Mattis in the 1960’s. The second model is the space–time percolation process, which is closely related to the contact model for the spread of disease. In Chapter 2 we define the appropriate space–time random-cluster model and explore a range of useful probabilistic techniques for studying it. The space– time Potts model emerges as a natural generalization of the quantum Ising model. The basic properties of the phase transitions in these models are treated in this chapter, such as the fact that there is at most one unbounded fk-cluster, and the resulting lower bound on the critical value in .

    In Chapter 3 we develop an alternative graphical representation of the quantum Ising model, called the random-parity representation. This representation is based on the random-current representation of the classical Ising model, and allows us to study in much greater detail the phase transition and critical behaviour. A major aim of this chapter is to prove sharpness of the phase transition in the quantum Ising model—a central issue in the theory— and to establish bounds on some critical exponents. We address these issues by using the random-parity representation to establish certain differential inequalities, integration of which gives the results.

    In Chapter 4 we explore some consequences and possible extensions of the results established in Chapters 2 and 3. For example, we determine the critical point for the quantum Ising model in and in ‘star-like’ geometries.

  • 31.
    Björner, Anders
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Vorwerk, Kathrin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    On the connectivity of manifold graphs2015In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 143, no 10, 4123-4132 p.Article in journal (Refereed)
    Abstract [en]

    This paper is concerned with lower bounds for the connectivity of graphs (one-dimensional skeleta) of triangulations of compact manifolds. We introduce a structural invariant b_M for simplicial d-manifolds M taking values in the range 0 <= b_M <= d-1. The main result is that b_M influences connectivity in the following way: The graph of a d-dimensional simplicial compact manifold M is (2d - b_M)-connected. The parameter b_M has the property that b_M = 0 if the complex M is flag. Hence, our result interpolates between Barnette's theorem (1982) that all d-manifold graphs are (d+1)-connected and Athanasiadis' theorem (2011) that flag d-manifold graphs are 2d-connected. The definition of b_M involves the concept of banner triangulations of manifolds, a generalization of flag triangulations.

  • 32. Bogart, Tristram
    et al.
    Haase, Christian
    Hering, Milena
    Lorenz, Benjamin
    Nill, Benjamin
    Stockholm University, Faculty of Science, Department of Mathematics.
    Paffenholz, Andreas
    Rote, Günter
    Santos, Francisco
    Schenck, Hal
    Finitely many smooth d-polytopes with n lattice points2015In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 207, no 1, 301-329 p.Article in journal (Refereed)
    Abstract [en]

    We prove that for fixed n there are only finitely many embeddings of ℚ-factorial toric varieties X into ℙ n that are induced by a complete linear system. The proof is based on a combinatorial result that implies that for fixed nonnegative integers d and n, there are only finitely many smooth d-polytopes with n lattice points. We also enumerate all smooth 3-polytopes with ≤ 12 lattice points.

  • 33.
    Borgefors, Gunilla
    Uppsala University, Interfaculty Units, Centre for Image Analysis. Uppsala University, Interfaculty Units, Centre for Image Analysis. Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis.
    Kedjekod - ett sätt att beskriva former i digitala bilder2005In: Problemlösning är # 1, Liber, Stockholm , 2005, 38-42 p.Chapter in book (Other scientific)
  • 34.
    Bras-Amorós, Maria
    et al.
    Universitat Rovira i Virgili, Catalonia, Spain.
    Domingo-Ferrer, Josep
    Universitat Rovira i Virgili, Catalonia, Spain.
    Stokes, Klara
    Universitat Rovira i Virgili, Catalonia, Spain.
    Configuraciones combinatóricas y recuperación privada de información por pares2009Conference paper (Other academic)
  • 35.
    Bras-Amorós, Maria
    et al.
    Universitat Rovira i Virgili, Tarragona, Catalonia, Spain .
    Stokes, Klara
    Universitat Rovira i Virgili, Tarragona, Catalonia, Spain .
    The semigroup of combinatorial configurations2012In: Semigroup Forum, ISSN 0037-1912, E-ISSN 1432-2137, Vol. 84, no 1, 91-96 p.Article in journal (Refereed)
    Abstract [en]

    We elaborate on the existence and construction of the so-called combinatorial configurations. The main result is that for fixed degrees the existence of such configurations is given by a numerical semigroup. The proof is constructive giving a method to obtain combinatorial configurations with parameters large enough.

  • 36.
    Bras-Amorós, Maria
    et al.
    Universitat Rovira i Virgili, Tarragona, Catalonia, Spain.
    Stokes, Klara
    Universitat Rovira i Virgili, Tarragona, Catalonia, Spain.
    On the existence of combinatorial configurations2010In: 3rd International Workshop on Optimal Networks Topologies, 2010, 2010, 145-167 p.Conference paper (Other academic)
  • 37.
    Bras-Amorós, Maria
    et al.
    Universitat Rovira i Virgili, Tarragona, Catalonia, Spain.
    Stokes, Klara
    Universitat Rovira i Virgili, Tarragona, Catalonia, Spain.
    Greferath, Marcus
    University College Dublin, Ireland.
    Problems related to combinatorial configurations with applications to P2P-user private information retrieval2010Conference paper (Other academic)
  • 38.
    Brattström, Gudrun
    Stockholm University, Faculty of Science, Department of Mathematics. Matematik.
    Leonardo da Pisa: Inger Christensen och Fibonacci2008In: Lyrikvännen, ISSN 0460-0762, Vol. 55, no 6, 33-38 p.Article in journal (Other (popular science, discussion, etc.))
    Abstract [sv]

    Den danska poeten Inger Christensen byggde sin diktsamling Alfabet på Fibonaccis talserie. Artikeln är en kort historisk essä över Fibonacci, och beskriver även hur talserien är konstruerad.

  • 39.
    Burdakov, Oleg
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Doherty, Patrick
    Linköping University, Department of Computer and Information Science, Artificial Intelligence and Integrated Computer Systems. Linköping University, The Institute of Technology.
    Kvarnström, Jonas
    Linköping University, Department of Computer and Information Science, Artificial Intelligence and Integrated Computer Systems. Linköping University, The Institute of Technology.
    Local Search for Hop-constrained Directed Steiner Tree Problem with Application to UAV-based Multi-target Surveillance2014In: Examining Robustness and Vulnerability of Networked Systems / [ed] Butenko, S., Pasiliao, E.L., Shylo, V., IOS Press, 2014, 26-50 p.Conference paper (Refereed)
    Abstract [en]

    We consider the directed Steiner tree problem (DSTP) with a constraint on the total number of arcs (hops) in the tree. This problem is known to be NP-hard, and therefore, only heuristics can be applied in the case of its large-scale instances.For the hop-constrained DSTP, we propose local search strategies aimed at improving any heuristically produced initial Steiner tree. They are based on solving a sequence of hop-constrained shortest path problems for which we have recently developed efficient label correcting algorithms.The presented approach is applied to finding suitable 3D locations where unmanned aerial vehicles (UAVs) can be placed to relay information gathered in multi-target monitoring and surveillance. The efficiency of our algorithms is illustrated by results of numerical experiments involving problem instances with up to 40 000 nodes and up to 20 million arcs.

  • 40.
    Burdakov, Oleg
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Doherty, Patrick
    Linköping University, Department of Computer and Information Science, Artificial Intelligence and Integrated Computer Systems. Linköping University, The Institute of Technology.
    Kvarnström, Jonas
    Linköping University, Department of Computer and Information Science, Artificial Intelligence and Integrated Computer Systems. Linköping University, The Institute of Technology.
    Local Search for Hop-constrained Directed Steiner Tree Problem with Application to UAV-based Multi-target Surveillance2014Report (Other academic)
    Abstract [en]

    We consider the directed Steiner tree problem (DSTP) with a constraint on the total number of arcs (hops) in the tree. This problem is known to be NP-hard, and therefore, only heuristics can be applied in the case of its large-scale instances.   For the hop-constrained DSTP, we propose local search strategies aimed at improving any heuristically produced initial Steiner tree. They are based on solving a sequence of hop-constrained shortest path problems for which we have recently developed ecient label correcting algorithms.   The presented approach is applied to nding suitable 3D locations where unmanned aerial vehicles (UAVs) can be placed to relay information gathered in multi-target monitoring and surveillance. The eciency of our algorithms is illustrated by results of numerical experiments involving problem instances with up to 40 000 nodes and up to 20 million arcs.

  • 41.
    Burke, Kyle
    et al.
    Plymouth State University, NH, USA.
    Demaine, Erik D.
    MIT, MA, USA.
    Gregg, Harrison
    Bard Coll Simons Rock, MA, USA.
    Hearn, Robert A.
    Portola Valley, CA USA.
    Hesterberg, Adam
    MIT, MA, USA.
    Hoffmann, Michael
    Swiss Federal Institute Technology, Switzerland.
    Ito, Hiro
    The University of Electro-Communications, Chofu, Japan.
    Kostitsyna, Irina
    University of Iibre Bruxelles, Belgium.
    Leonard, Jody
    Bard Coll Simons Rock, MA, USA.
    Loeffler, Maarten
    University of Utrecht, Netherlands.
    Santiago, Aaron
    Bard Coll Simons Rock, MA, USA.
    Schmidt, Christiane
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering. University of Elect Communicat, Japan.
    Uehara, Ryuhei
    Japan Adv Institute Science and Technology, Japan.
    Uno, Yushi
    Osaka Prefecture University, Japan.
    Williams, Aaron
    Bard Coll Simons Rock, MA, USA.
    Single-Player and Two-Player Buttons & Scissors Games2016In: DISCRETE AND COMPUTATIONAL GEOMETRY AND GRAPHS, JCDCGG 2015, SPRINGER INT PUBLISHING AG , 2016, Vol. 9943, 60-72 p.Conference paper (Refereed)
    Abstract [en]

    We study the computational complexity of the Buttons amp; Scissors game and obtain sharp thresholds with respect to several parameters. Specifically we show that the game is NP-complete for C = 2 colors but polytime solvable for C = 1. Similarly the game is NP-complete if every color is used by at most F = 4 buttons but polytime solvable for F amp;lt;= 3. We also consider restrictions on the board size, cut directions, and cut sizes. Finally, we introduce several natural two-player versions of the game and show that they are PSPACE-complete.

  • 42.
    Carling, Kenneth
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Han, Mengjie
    Dalarna University, School of Technology and Business Studies, Statistics.
    Håkansson, Johan
    Dalarna University, School of Technology and Business Studies, Information Systems.
    Rebreyend, Pascal
    Dalarna University, School of Technology and Business Studies, Computer Engineering.
    Testing the gravity p-median model empirically2015In: Operations Research Perspectives, ISSN 2214-7160, Vol. 2, no 124, 132Article in journal (Refereed)
    Abstract [en]

    Regarding the location of a facility, the presumption in the widely used p-median model is that the customer opts for the shortest route to the nearest facility. However, this assumption is problematic on free markets since the customer is presumed to gravitate to a facility by the distance to and the attractiveness of it. The recently introduced gravity p-median model offers an extension to the p-median model that account for this. The model is therefore potentially interesting, although it has not yet been implemented and tested empirically. In this paper, we have implemented the model in an empirical problem of locating vehicle inspections, locksmiths, and retail stores of vehicle spare-parts for the purpose of investigating its superiority to the p-median model. We found, however, the gravity p-median model to be of limited use for the problem of locating facilities as it either gives solutions similar to the p-median model, or it gives unstable solutions due to a non-concave objective function.

  • 43.
    Casselgren, Carl Johan
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    On avoiding some families of arrays2012In: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 312, no 5, 963-972 p.Article in journal (Refereed)
    Abstract [en]

    An n×n array A with entries from {1,…,n} is avoidable if there is an n×n Latin square L such that no cell in L contains a symbol that occurs in the corresponding cell in A. We show that the problem of determining whether an array that contains at most two entries per cell is avoidable is NP-complete, even in the case when the array has entries from only two distinct symbols. Assuming that PNP, this disproves a conjecture by Öhman. Furthermore, we present several new families of avoidable arrays. In particular, every single entry array (arrays where each cell contains at most one symbol) of order n≥2k with entries from at most k distinct symbols and where each symbol occurs in at most n−2 cells is avoidable, and every single entry array of order n, where each of the symbols 1,…,n occurs in at most cells, is avoidable. Additionally, if k≥2, then every single entry array of order at least n≥4, where at most k rows contain non-empty cells and where each symbol occurs in at most nk+1 cells, is avoidable.

  • 44.
    Casselgren, Carl Johan
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    On some graph coloring problems2011Doctoral thesis, comprehensive summary (Other academic)
  • 45.
    Casselgren, Carl Johan
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Haggkvist, Roland
    Umeå University, Sweden.
    Coloring Complete and Complete Bipartite Graphs from Random Lists2016In: Graphs and Combinatorics, ISSN 0911-0119, E-ISSN 1435-5914, Vol. 32, no 2, 533-542 p.Article in journal (Refereed)
    Abstract [en]

    Assign to each vertex v of the complete graph on n vertices a list L(v) of colors by choosing each list independently and uniformly at random from all f(n)-subsets of a color set , where f(n) is some integer-valued function of n. Such a list assignment L is called a random (f(n), [n])-list assignment. In this paper, we determine the asymptotic probability (as ) of the existence of a proper coloring of , such that for every vertex v of . We show that this property exhibits a sharp threshold at . Additionally, we consider the corresponding problem for the line graph of a complete bipartite graph with parts of size m and n, respectively. We show that if , , and L is a random (f(n), [n])-list assignment for the line graph of , then with probability tending to 1, as , there is a proper coloring of the line graph of with colors from the lists.

  • 46. Casselgren, Carl Johan
    et al.
    Häggkvist, Roland
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Completing partial Latin squares with one filled row, column and symbol2013In: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 313, no 9, 1011-1017 p.Article in journal (Refereed)
    Abstract [en]

    Let P be an n x n partial Latin square every non-empty cell of which lies in a fixed row r, a fixed column c or contains a fixed symbols. Assume further that s is the symbol of cell (r, c) in P. We prove that P is completable to a Latin square if n >= 8 and n is divisible by 4, or n <= 7 and n is not an element of {3, 4, 5}. Moreover, we present a polynomial algorithm for the completion of such a partial Latin square. (C) 2013 Elsevier B.V. All rights reserved.

  • 47. Casselgren, Carl Johan
    et al.
    Häggkvist, Roland
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Coloring Complete and Complete Bipartite Graphs from Random Lists2016In: Graphs and Combinatorics, ISSN 0911-0119, E-ISSN 1435-5914, Vol. 32, no 2, 533-542 p.Article in journal (Refereed)
    Abstract [en]

    Assign to each vertex v of the complete graph on n vertices a list L(v) of colors by choosing each list independently and uniformly at random from all f(n)-subsets of a color set , where f(n) is some integer-valued function of n. Such a list assignment L is called a random (f(n), [n])-list assignment. In this paper, we determine the asymptotic probability (as ) of the existence of a proper coloring of , such that for every vertex v of . We show that this property exhibits a sharp threshold at . Additionally, we consider the corresponding problem for the line graph of a complete bipartite graph with parts of size m and n, respectively. We show that if , , and L is a random (f(n), [n])-list assignment for the line graph of , then with probability tending to 1, as , there is a proper coloring of the line graph of with colors from the lists.

  • 48.
    Casselgren, Carl Johan
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Sune Pedersen, Anders
    University of Southern Denmark, Denmark; Aarhus University Hospital, Denmark.
    Hadwigers Conjecture for inflations of 3-chromatic graphs2016In: European journal of combinatorics (Print), ISSN 0195-6698, E-ISSN 1095-9971, Vol. 51, 99-108 p.Article in journal (Refereed)
    Abstract [en]

    Hadwigers Conjecture states that every k-chromatic graph has a complete minor of order k. A graph G is an inflation of a graph G if G is obtained from G by replacing each vertex upsilon of G by a clique C-upsilon and joining two vertices of distinct cliques by an edge if and only if the corresponding vertices of G are adjacent. We present an algorithm for computing an upper bound on the chromatic number chi (G) of any inflation G of any 3-chromatic graph G. As a consequence, we deduce that Hadwigers Conjecture holds for any inflation of any 3-colorable graph. (C) 2015 Elsevier Ltd. All rights reserved.

  • 49.
    Casselgren, Carl Johan
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering. University of Southern Denmark, Denmark.
    Toft, Bjarne
    University of Southern Denmark, Denmark.
    One-sided interval edge-colorings of bipartite graphs2016In: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 339, no 11, 2628-2639 p.Article in journal (Refereed)
    Abstract [en]

    Let G be a bipartite graph with bipartition (X, Y). An X-interval coloring of G is a proper edge-coloring of G by integers such that the colors on the edges incident to any vertex in X form an interval. Denote by chi(int)(G, X) the minimum k such that G has an X-interval coloring with k colors. In this paper we give various upper and lower bounds on chi(int)(G, X) in terms of the vertex degrees of G. We also determine chi(int) (G, X) exactly for some classes of bipartite graphs G. Furthermore, we present upper bounds on chi(int) (G, X) for classes of bipartite graphs G with maximum degree Delta(G) at most 9: in particular, if Delta(G) = 4, then chi(int) (G, X) amp;lt;= 6; if Delta(G) = 5, then chi(int) (G, X) amp;lt;= 15; if Delta(G) = 6, then chi(int) (G, X) amp;lt;= 33. (C) 2016 Elsevier B.V. All rights reserved.

    The full text will be freely available from 2018-06-06 13:17
  • 50.
    Christofides, Demetres
    et al.
    School of Computing and Mathematics, UCLan Cyprus, Pyla, Cyprus.
    Markström, Klas
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    The thresholds for diameter 2 in random Cayley graphs2014In: Random structures & algorithms (Print), ISSN 1042-9832, E-ISSN 1098-2418, Vol. 45, no 2, 218-235 p.Article in journal (Refereed)
1234567 1 - 50 of 335
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