Wang Weifan

Edge choosability of planar graphs without short cycles

In this paper we prove that if G is a planar graph with Δ=5 and without 4-cycles or 6-cycles, then G is edge-6-choosable. This consequence together with known results show that, for each fixed k ∈{3,4,5,6}, a k -cycle-free planar graph G is edge-(Δ+1)-choosable, where Δ denotes the maximum degree of G .