Abstract
A proper vertex k-coloring of a graph G is called dynamic, if there is no vertex v∈V(G) with d(v)≥2 and all of its neighbors have the same color. The smallest integer k such that G has a k-dynamic coloring is called the dynamic chromatic number of G and denoted by χ2(G). We say that v∈V(G) in a proper vertex coloring of G is a bad vertex if d(v)≥2 and only one color appears in the neighbors of v. In this paper, we show that if G is a graph with the chromatic number at least 6, then there exists a proper vertex χ(G)-coloring of G such that the set of bad vertices of G is an independent set. Also, we provide some upper bounds for χ2(G)−χ(G) in terms of some parameters of the graph G.
Published Version
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