Acyclic edge coloring of planar graphs with large girth

Acyclic coloring problem is a specialized problem that arises in the efficient computation of Hessians. A proper edge coloring of a graph G is called acyclic if there is no 2-colored cycle in G. The acyclic edge chromatic number of G is the least number of colors in an acyclic edge coloring of G. Alon et al. conjectured that . In this paper, we consider the sufficient conditions for the planar graphs satisfying and .