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Journal of Combinatorial Optimization

, Volume 35, Issue 2, pp 555–562 | Cite as

List-edge-coloring of planar graphs without 6-cycles with three chords

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Abstract

A graph G is edge-k-choosable if, whenever we are given a list L(e) of colors with \(|L(e)|\ge k\) for each \(e\in E(G)\), we can choose a color from L(e) for each edge e such that no two adjacent edges receive the same color. In this paper we prove that if G is a planar graph, and each 6-cycle contains at most two chords, then G is edge-k-choosable, where \(k=\max \{8,\Delta (G)+1\}\), and edge-t-choosable, where \(t=\max \{10,\Delta (G)\}\).

Keywords

Edge-choosable List-edge-chromatic-number Cycle Planar graph 

Notes

Acknowledgements

We would like to thank the referees for providing some very helpful comments and suggestions for revising this paper.

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.School of ScienceChina University of Geosciences (Beijing)BeijingChina
  2. 2.School of MathematicsShandong UniversityJinanChina

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