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A note on path factors of (3,4)-biregular bipartite graphs
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2011 (English)In: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 18, no 1, P218- p.Article in journal (Refereed) Published
Abstract [en]

A proper edge coloring of a graph G with colors 1,2,3, ... is called an interval coloring if the colors on the edges incident with any vertex are consecutive. A bipartite graphis (3,4)-biregular if all vertices in one part have degree 3 and all vertices in the other part have degree 4. Recently it was proved [J. Graph Theory 61 (2009), 88-97] that if such a graph G has a spanning subgraph whose components are paths with end points at 3-valent vertices and lengths in {2,4,6,8}, then G has an interval coloring. It was also conjectured that every simple (3,4)-biregular bipartite graph has such a subgraph. We provide some evidence for this conjecture by proving that a simple (3,4)-biregular bipartite graph has a spanning subgraph whose components are nontrivial paths with endpoints at 3-valent vertices and lengths not exceeding 22.

Place, publisher, year, edition, pages
2011. Vol. 18, no 1, P218- p.
Keyword [en]
path factor, biregular bipartite graph, interval edge coloring
National Category
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-50410ISI: 000296974200001OAI: oai:DiVA.org:umu-50410DiVA: diva2:464281
Available from: 2011-12-13 Created: 2011-12-08 Last updated: 2017-12-08Bibliographically approved

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