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l-Degree Turan Density
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2014 (English)In: SIAM Journal on Discrete Mathematics, ISSN 0895-4801, E-ISSN 1095-7146, Vol. 28, no 3, 1214-1225 p.Article in journal (Refereed) Published
Abstract [en]

Let H-n be a k-graph on n vertices. For 0 <= l < k and an l-subset T of V (H-n), define the degree deg(T) of T to be the number of (k - l)-subsets S such that S boolean OR T is an edge in H-n. Let the minimum l-degree of H-n be delta(l) (H-n) = min{deg(T) : T subset of V (H-n) and vertical bar T vertical bar = l}. Given a family F of k-graphs, the l-degree Turan number ex(l) (n, F) is the largest delta(l) (H-n) over all F-free k-graphs H-n on n vertices. Hence, ex(0) (n, F) is the Turan number. We define l-degree Turan density to be pi(kappa)(l) (F) = lim sup(n ->infinity) ex(l)(n, F)/kappa(n-l). In this paper, we show that for k > l > 1, the set of pi(kappa)(l) (F) is dense in the interval [0, 1). Hence, there is no "jump" for l-degree Turan density when k > l > 1. We also give a lower bound on pi(kappa)(l) (F) in terms of an ordinary Turan density.

Place, publisher, year, edition, pages
2014. Vol. 28, no 3, 1214-1225 p.
National Category
Discrete Mathematics
URN: urn:nbn:se:umu:diva-92706DOI: 10.1137/120895974ISI: 000343230800012OAI: diva2:742346
Available from: 2014-09-01 Created: 2014-09-01 Last updated: 2015-07-30Bibliographically approved

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Markström, Klas
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