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arXiv · 1205.6869

A new upper bound on the acyclic chromatic indices of planar graphs

Weifan Wang·Qiaojun Shu·Yiqiao Wang
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Abstract

An acyclic edge coloring of a graph $G$ is a proper edge coloring such that no bichromatic cycles are produced. The acyclic chromatic index $a'(G)$ of $G$ is the smallest integer $k$ such that $G$ has an acyclic edge coloring using $k$ colors. It was conjectured that $a'(G)\le \Delta+2$ for any simple graph $G$ with maximum degree $\Delta$. In this paper, we prove that if $G$ is a planar graph, then $a'(G)\leq\Delta +7$. This improves a result by Basavaraju et al. [{\em Acyclic edge-coloring of planar graphs}, SIAM J. Discrete Math., 25 (2011), pp. 463-478], which says that every planar graph $G$ satisfies $a'(G)\leq\Delta +12$.

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Weifan Wang, Qiaojun Shu, Yiqiao Wang. 2012-05-31. A new upper bound on the acyclic chromatic indices of planar graphs. https://arxiv.org/abs/1205.6869

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