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On Interval Edge Colorings of Biregular Bipartite Graphs With Small Vertex Degrees
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
University of Southern Denmark, Denmark.
2015 (English)In: Journal of Graph Theory, ISSN 0364-9024, E-ISSN 1097-0118, Vol. 80, no 2, 83-97 p.Article in journal (Refereed) Published
Abstract [en]

A proper edge coloring of a graph with colors 1, 2, 3, ... is called an interval coloring if the colors on the edges incident to each vertex form an interval of integers. A bipartite graph is (a,b)-biregular if every vertex in one part has degree a and every vertex in the other part has degree b. It has been conjectured that all such graphs have interval colorings. We prove that all (3, 6)-biregular graphs have interval colorings and that all (3, 9)-biregular graphs having a cubic subgraph covering all vertices of degree 9 admit interval colorings. Moreover, we prove that slightly weaker versions of the conjecture hold for (3, 5)-biregular, (4, 6)-biregular, and (4, 8)-biregular graphs. All our proofs are constructive and yield polynomial time algorithms for constructing the required colorings. (C) 2014 Wiley Periodicals, Inc.

Place, publisher, year, edition, pages
Wiley: 12 months , 2015. Vol. 80, no 2, 83-97 p.
Keyword [en]
biregular graph; interval edge coloring
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-121093DOI: 10.1002/jgt.21841ISI: 000359380300001OAI: oai:DiVA.org:liu-121093DiVA: diva2:852018
Note

Funding Agencies|SVeFUM

Available from: 2015-09-07 Created: 2015-09-07 Last updated: 2017-12-04

Open Access in DiVA

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