Coloring quasi-line graphs

Authors:
Maria Chudnovsky;Alexandra Ovetsky
Affiliations:
Department of Mathematics, Princeton University Princeton, NJ 08544;Department of Mathematics, Princeton University Princeton, NJ 08544
Venue:
Journal of Graph Theory
Year:
2007

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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 This research was conducted while the author served as a Clay Mathematics Institute Research Fellow.