Coloring quasi-line graphs

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 paper we extend this result to all quasi-line graphs. We also show that this bound is tight.

• Type: Journal
• Year: 2007
• Where: JGT
• Authors: Maria Chudnovsky, Alexandra Ovetsky
• Keywords: JGT 2007, Line Graph, Proper Superset, Quasi-line Graphs