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 3/2ω(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.