Further result on acyclic chromatic index of planar graphs

An acyclic edge coloring of a graph GG 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 GG is the least number of colors in an acyclic edge coloring of GG. It was conjectured that χa′(G)≤Δ(G)+2 for any simple graph GG with maximum degree Δ(G)Δ(G). In this paper, we prove that every planar graph GG admits an acyclic edge coloring with Δ(G)+6Δ(G)+6 colors.