Acyclic edge coloring of planar graphs without cycles of specific lengths

摘要

A proper edge coloring of a graph G is called acyclic edge coloring if there are no bicolored cycles in G. Let Δ(G) denote the maximum degree of G. In this paper, we prove that every planar graph with Δ(G)≥10 and without cycles of lengths 4 to 11 is acyclic (Δ(G)+1)-edge colorable, and every planar graph with Δ(G)≥11 and without cycles of lengths 4 to 9 is acyclic (Δ(G)+1)-edge colorable.