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

Abstract

Some structural properties of planar graphs without 4-cycles are investigated. By the structural properties, it is proved that every planar graph G without 4-cycles is edge-(Δ (G) + 1)-choosable, which perfects the result given by Zhang and Wu: If G is a planar graph without 4-cycles, then G is edge-t-choosable, where t = 7 if Δ (G) = 5, and otherwise t = Δ (G) + 1. © 2007 Elsevier B.V. All rights reserved.