Edge-choosability of planar graphs without non-induced 5-cycles

Abstract

A graph G is edge-L-colorable, if for a given edge assignment L = {L (e) : e ∈ E (G)}, there exits a proper edge-coloring φ{symbol} of G such that φ{symbol} (e) ∈ L (e) for all e ∈ E (G). If G is edge-L-colorable for every edge assignment L with | L (e) | ≥ k for e ∈ E (G), then G is said to be edge-k-choosable. In this paper, we prove that if G is a planar graph without non-induced 5-cycles, then G is edge-k-choosable, where k = max {7, Δ (G) + 1}. © 2008 Elsevier B.V. All rights reserved.