Coloring (4K1,C4,C6)-free graphs

Abstract

(4K1,C4,C6)-free graphs are precisely the even-hole-free graphs of stability number at most three. We show that (4K1,C4,C6)-free graphs can be recognized in O(n3) time, and furthermore, that all the following can be computed in O(n3) time for such graphs: an optimal coloring, a minimum clique cover, and the list of all maximal cliques. We also show that every (4K1,C4,C6)-free graph on n vertices has at most n maximal cliques.