Abstract
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.
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Communicated by Behruz Tayfeh-Rezaie.
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Omoomi, B., Taleb, M. Clique-Coloring of \(K_{3,3}\)-Minor Free Graphs. Bull. Iran. Math. Soc. 46, 1539–1550 (2020). https://doi.org/10.1007/s41980-019-00341-0
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DOI: https://doi.org/10.1007/s41980-019-00341-0