Advanced Search

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 ${\chi }_b\left(G\right)$ 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 $\chi \left(G\right)\le k\le {\chi }_b\left(G\right)$. In this paper, we establish four general upper bounds on ${\chi }_b\left(G\right)$. We present results on the b-chromatic number...