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The entire choosability of plane graphs

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Journal of Combinatorial Optimization Aims and scope Submit manuscript

Abstract

A plane graph\(G\) is entirely\(k\)-choosable if, for every list\(L\) of colors satisfying\(L(x)=k\) for all\(x\in V(G)\cup E(G) \cup F(G)\), there exists a coloring which assigns to each vertex, each edge and each face a color from its list so that any adjacent or incident elements receive different colors. In 1993, Borodin proved that every plane graph\(G\) with maximum degree\(\Delta \ge 12\) is entirely\((\Delta +2)\)-choosable. In this paper, we improve this result by replacing 12 by 10.

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Acknowledgments

The authors would like to thank the referees for their valuable comments that helped to improve this work. Weifan Wang: Research supported by NSFC (No. 11371328). Yiqiao Wang: Research supported by NSFC (No. 11301035)

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China

    Weifan Wang, Tingting Wu & Xiaoxue Hu

  2. School of Management, Beijing University of Chinese Medicine, Beijing, 100029, China

    Yiqiao Wang

Authors
  1. Weifan Wang

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  2. Tingting Wu

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  3. Xiaoxue Hu

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  4. Yiqiao Wang

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Corresponding author

Correspondence toWeifan Wang.

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