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Coloring quasi-line graphs

✍ Scribed by Maria Chudnovsky; Alexandra Ovetsky

Publisher: John Wiley and Sons
Year: 2006
Tongue: English
Weight: 127 KB
Volume: 54
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.20192

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✦ Synopsis

Abstract

A graph G is a quasi‐line graph if for every vertex v, the set of neighbors of v can be expressed as the union of two cliques. The class of quasi‐line graphs is a proper superset of the class of line graphs. A theorem of Shannon's implies that if G is a line graph, then it can be properly colored using no more than 3/2 ω(G) colors, where ω(G) is the size of the largest clique in G. In this article, we extend this result to all quasi‐line graphs. We also show that this bound is tight. © 2006 Wiley Periodicals, Inc. J Graph Theory

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