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Journal of Combinatorial Optimization

, Volume 31, Issue 3, pp 1013–1022 | Cite as

A note on the minimum number of choosability of planar graphs

  • Huijuan Wang
  • Lidong Wu
  • Xin Zhang
  • Weili Wu
  • Bin LiuEmail author
Article

Abstract

The problem of minimum number of choosability of graphs was first introduced by Vizing. It appears in some practical problems when concerning frequency assignment. In this paper, we study two important list coloring, list edge coloring and list total coloring. We prove that \(\chi '_{l}(G)=\varDelta \) and \(\chi ''_{l}(G)=\varDelta +1\) for planar graphs with \(\varDelta \ge 8\) and without adjacent 4-cycles.

Keywords

Choosability Planar graph Cycle List edge coloring 

Notes

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China under Grants 11201440, 11271006, 11301410, the Natural Science Basic Research Plan in Shaanxi Province of China under Grant 2013JQ1002, and the Scientific Research Foundation for the Excellent Young and Middle-Aged Scientists of Shandong Province of China under Grant BS2013DX002. This work was also supported in part by the National Science Foundation of USA under Grants CNS-0831579 and CCF-0728851.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Huijuan Wang
    • 1
  • Lidong Wu
    • 2
  • Xin Zhang
    • 3
  • Weili Wu
    • 4
    • 5
  • Bin Liu
    • 6
    Email author
  1. 1.College of MathematicsQingdao UniversityQingdaoChina
  2. 2.Department of Computer ScienceUniversity of Texas at TylerTylerUSA
  3. 3.School of Mathematics and StatisticsXidian UniversityXi’anChina
  4. 4.College of Computer Science and TechnologyTaiyuan University of TechnologyTaiyuanChina
  5. 5.Department of Computer ScienceUniversity of Texas at DallasRichardsonUSA
  6. 6.Department of MathematicsOcean University of ChinaQingdaoChina

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