Edge-choosability of planar graphs without chordal 6-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 of G such that φ⋯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 chordal 6-cycles, then G is edge-k-choosable, where k = max{8, △(G) + 1}.