ACYCLIC LIST EDGE COLORING OF PLANAR GRAPHS

A proper edge coloring of a graph is said to be acyclic if any cycle is colored with at least three colors. The acyclic chromatic index, denoted a'(G), is the least number of colors required for an acyclic edge coloring of G. An edge-list L of a graph G is a mapping that assigns a finite set of positive integers to each edge of G. An acyclic edge coloring phi of G such that phi(e) is an element of L(e) for any e is an element of E(G) is called an acyclic L-edge coloring of G. A graph G is said to be acyclically k-edge choosable if it has an acyclic L-edge coloring for any edge-list L that satisfies | L(e)| >= k for each edge e. The acyclic list chromatic index is the least integer k such that G is acyclically k-edge choosable. In [2, 3, 4, 7, 10, 11, 12], upper bounds for the acyclic chromatic index of several classes of planar graphs were obtained. In this paper, we generalize these results to the acyclic list chromatic index of planar graphs.