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Upper bounds on the b-chromatic number and results for restricted graph classes

Mais AlkhateebAnja Kohl — 2011

Discussiones Mathematicae Graph Theory

A b-coloring of a graph G by k colors is a proper vertex coloring such that every color class contains a color-dominating vertex, that is, a vertex having neighbors in all other k-1 color classes. The b-chromatic number χ b ( G ) is the maximum integer k for which G has a b-coloring by k colors. Moreover, the graph G is called b-continuous if G admits a b-coloring by k colors for all k satisfying χ ( G ) k χ b ( G ) . In this paper, we establish four general upper bounds on χ b ( G ) . We present results on the b-chromatic number...

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