Acyclic edge coloring of planar graphs with Δ colors

An acyclic edge coloring of a graph is a proper edge coloring without bichromatic cycles. In 1978, it was conjectured that @D(G)+2 colors suffice for an acyclic edge coloring of every graph G (Fiamcik, 1978 [8]). The conjecture has been verified for several classes of graphs, however, the best known upper bound for as special class as planar graphs are, is @D+12 (Basavaraju and Chandran, 2009 [3]). In this paper, we study simple planar graphs which need only @D(G) colors for an acyclic edge coloring. We show that a planar graph with girth g and maximum degree @D admits such acyclic edge coloring if g>=12, or g>=8 and @D>=4, or g>=7 and @D>=5, or g>=6 and @D>=6, or g>=5 and @D>=10. Our results improve some previously known bounds.