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arXiv · 0908.2237

Acyclic Edge coloring of Planar Graphs

Manu Basavaraju·L. Sunil Chandran
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Abstract

An $acyclic$ edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The \emph{acyclic chromatic index} of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and is denoted by $a'(G)$. It was conjectured by Alon, Sudakov and Zaks (and much earlier by Fiamcik) that $a'(G)\le Δ+2$, where $Δ=Δ(G)$ denotes the maximum degree of the graph. We prove that if $G$ is a planar graph with maximum degree $Δ$, then $a'(G)\le Δ+ 12$.

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Manu Basavaraju, L. Sunil Chandran. 2009-08-16. Acyclic Edge coloring of Planar Graphs. https://arxiv.org/abs/0908.2237

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