Structural properties and edge choosability of planar graphs without 4-cycles

Some structural properties of planar graphs without 4-cycles are investigated. By the structural properties, it is proved that every planar graph GG without 4-cycles is edge  -(Δ(G)+1)(Δ(G)+1)-choosable  , which perfects the result given by Zhang and Wu: If GG is a planar graph without 4-cycles, then GG is edge  -tt-choosable  , where t=7t=7 if Δ(G)=5Δ(G)=5, and otherwise t=Δ(G)+1t=Δ(G)+1.