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On interval edge colorings of (a, ß)-biregular bipartite graphs
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
Department of Mathematics, UmeÅ University, SE-901 87 UmeÅ, Sweden.
2007 (English)In: Discrete Mathematics, ISSN 0012-365X, Vol. 307, no 15, 1951-1956 p.Article in journal (Refereed) Published
Abstract [en]

A bipartite graph G is called (a, ß)-biregular if all vertices in one part of G have degree a and all vertices in the other part have degree ß. An edge coloring of a graph G with colors 1, 2, 3, ..., t is called an interval t-coloring if the colors received by the edges incident with each vertex of G are distinct and form an interval of integers and at least one edge of G is colored i, for i = 1, ..., t. We show that the problem to determine whether an (a, ß)-biregular bipartite graph G has an interval t-coloring is NP-complete in the case when a = 6, ß = 3 and t = 6. It is known that if an (a, ß)-biregular bipartite graph G on m vertices has an interval t-coloring then a + ß - gcd (a, ß) = t = m - 1, where gcd (a, ß) is the greatest common divisor of a and ß. We prove that if an (a, ß)-biregular bipartite graph has m = 2 (a + ß) vertices then the upper bound can be improved to m - 3. © 2006 Elsevier B.V. All rights reserved.

Place, publisher, year, edition, pages
2007. Vol. 307, no 15, 1951-1956 p.
Keyword [en]
Bipartite graph, Edge coloring, Interval coloring, NP-complete problem
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-49122DOI: 10.1016/j.disc.2006.11.001OAI: diva2:270018
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2011-01-11

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Asratian, Armen
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