Authors:
L. Hu, L. Sun, J.-L. Wu
Title:
List coloring of planar graphs without 6-cycles with two chords
Source:
Discussiones Mathematicae Graph Theory
Received 22.05.2017, Revised 10.09.2018, Accepted 10.09.2018, doi: 10.7151/dmgt.2183

Abstract:
A graph G is edge-L-colorable if for a given edge assignment L={L(e):e∈E(G)}, there exists a proper edge-coloring φ of G such that φ(e)∈L(e) for all e∈E(G). If G is edge-L-colorable for every edge assignment L such that |L(e)|≥ k for all 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 6-cycles with two chords, then G is edge-k-choosable, where k=\max{7,Δ(G)+1}, and is edge-t-choosable, where t=\max{9,Δ(G)}.
Keywords:
planar graph, edge choosable, list edge chromatic number, chord

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