Clique-coloring of K_3,3-minor free graphs

01/07/2018

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by   Behnaz Omoomi, et al.

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A clique-coloring of a given graph G is a coloring of the vertices of G such that no maximal clique of size at least two is monocolored. The clique-chromatic number of G is the least number of colors for which G admits a clique-coloring. It has been proved that every planar graph is 3-clique colorable and every claw-free planar graph, different from an odd cycle, is 2-clique colorable. In this paper, we generalize these results to K_3,3-minor free (K_3,3-subdivision free) graphs.