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arXiv · 0908.2543

On Dynamic Coloring of Graphs

Meysam Alishahi
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Abstract

A dynamic coloring of a graph $G$ is a proper coloring such that for every vertex $v\in V(G)$ of degree at least 2, the neighbors of $v$ receive at least 2 colors. In this paper we present some upper bounds for the dynamic chromatic number of graphs. In this regard, we shall show that there is a constant $c$ such that for every $k$-regular graph $G$, $χ_d(G)\leq χ(G)+ c\ln k +1$. Also, we introduce an upper bound for the dynamic list chromatic number of regular graphs.

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Meysam Alishahi. 2009-08-18. On Dynamic Coloring of Graphs. https://arxiv.org/abs/0908.2543

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