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 χ a ′ ( 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 χ a ′ ( 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 .