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Journal of Combinatorial Optimization

, Volume 31, Issue 3, pp 1221–1240 | Cite as

The entire choosability of plane graphs

  • Weifan WangEmail author
  • Tingting Wu
  • Xiaoxue Hu
  • Yiqiao Wang
Article

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.

Keywords

Plane graph Entire choosability Maximum degree 

Notes

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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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Weifan Wang
    • 1
    Email author
  • Tingting Wu
    • 1
  • Xiaoxue Hu
    • 1
  • Yiqiao Wang
    • 2
  1. 1.Department of MathematicsZhejiang Normal UniversityJinhuaChina
  2. 2.School of ManagementBeijing University of Chinese MedicineBeijingChina

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