Abstract
We consider the problem of clique-coloring, that is coloring the vertices of a given graph such that no maximal clique of size at least 2 is monocolored. Whereas we do not know any odd-hole-free graph that is not 3-clique-colorable, the existence of a constant C such that any perfect graph is C-clique-colorable is an open problem. In this paper we solve this problem for some subclasses of odd-hole-free graphs: those that are diamond-free and those that are bull-free. We also prove the NP-completeness of 2-clique-coloring K4-free perfect graphs. © 2006 Wiley Periodicals, Inc. J Graph Theory 53: 233–249, 2006
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