Edge choosability of planar graphs without short cycles

In this paper we prove that ifG is a planar graph with Δ = 5 and without 4-cycles or 6-cycles, thenG is edge-6-choosable. This consequence together with known results show that, for each fixedk Є {3,4,5,6}, ak-cycle-free planar graphG is edge-(Δ + 1)-choosable, where Δ denotes the maximum degree ofG.