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arXiv · 1405.0713

Further result on acyclic chromatic index of planar graphs

Tao Wang·Yaqiong Zhang
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Abstract

An acyclic edge coloring of a graph $G$ is a proper edge coloring such that every cycle is colored with at least three colors. The acyclic chromatic index $\chiup_{a}'(G)$ of a graph $G$ is the least number of colors in an acyclic edge coloring of $G$. It was conjectured that $\chiup'_{a}(G)\leq Δ(G) + 2$ for any simple graph $G$ with maximum degree $Δ(G)$. In this paper, we prove that every planar graph $G$ admits an acyclic edge coloring with $Δ(G) + 6$ colors.

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Tao Wang, Yaqiong Zhang. 2015-08-26. Further result on acyclic chromatic index of planar graphs. https://doi.org/10.1016/j.dam.2015.07.015

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