An improved bound on acyclic chromatic index of planar graphs

A proper edge coloring of a graph G is called acyclic if there is no bichromatic cycle in G. The acyclic chromatic index of G, denoted by χa′(G), is the least number of colors k such that G has an acyclic k-edge-coloring. Basavaraju et al. [M. Basavaraju, L.S. Chandran, N. Cohen, F. Havet and T. Müller, Acyclic edge-coloring of planar graphs, SIAM Journal of Discrete Mathematics 25 (2) (2011) 463-478] showed that χa′(G)≤Δ(G)+12 for any planar graph G with maximum degree Δ(G). In this paper, the bound is improved to Δ(G)+10.