Acyclic edge coloring of planar graphs with girth at least 5

A proper edge coloring of a graph GG is acyclic if there is no bichromatic cycle in GG. The acyclic chromatic index of GG, denoted χa′(G), is the least number of colors kk such that GG has an acyclic kk-edge-coloring. In this paper, it is shown that if GG is a planar graph with girth at least 5 and maximum degree ΔΔ, then χa′(G)≤Δ+1. Moreover, if Δ≥9Δ≥9, then χa′(G)=Δ.