Abstract
A graph \(G\) is edge-\(L\)-colorable if for a given edge assignment \(L=\{L(e):e\in E(G)\}\), there exits a proper edge-coloring \(\phi \) of \(G\) such that \(\phi (e)\in L(e)\) for all \(e\in E(G)\). If \(G\) is edge-\(L\)-colorable for every edge assignment \(L\) with \(| L(e)|\ge k\) for \(e\in E(G)\), then \(G\) is said to be edge-\(k\)-choosable. In this paper, we prove that if \(G\) is a planar graph without non-induced \(6\)-cycles, then \(G\) is edge-\(k\)-choosable, where \(k=\max \{8, \Delta (G)+1\}\).
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We would like to thank the referees for providing some very helpful comments and suggestions for revising this paper.
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This work is supported by SDNSF (No. ZR2013AM001).
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Cai, J. List Edge Coloring of Planar Graphs Without Non-Induced 6-Cycles. Graphs and Combinatorics 31, 827–832 (2015). https://doi.org/10.1007/s00373-014-1420-6
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DOI: https://doi.org/10.1007/s00373-014-1420-6