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On the difference between chromatic number and dynamic chromatic number of graphs
Ahadi, A ; Sharif University of Technology | 2012
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- Type of Document: Article
- DOI: 10.1016/j.disc.2011.09.006
- Publisher: Elsevier , 2012
- 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
- Keywords:
- Dynamic coloring ; Independent number ; Vertex coloring
- Source: Discrete Mathematics ; Volume 312, Issue 17 , September , 2012 , Pages 2579-2583 ; 0012365X (ISSN)
- URL: http://www.sciencedirect.com/science/article/pii/S0012365X11004109