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 χa′(G) of a graph G is the least number of colors in an acyclic edge coloring of G. It was conjectured that χa′(G)≤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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