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A note on the minimum number of choosability of planar graphs

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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.

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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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Authors and Affiliations

  1. College of Mathematics, Qingdao University, Qingdao, 266071, China

    Huijuan Wang

  2. Department of Computer Science, University of Texas at Tyler, Tyler, TX, 75799, USA

    Lidong Wu

  3. School of Mathematics and Statistics, Xidian University, Xi’an, 710071, China

    Xin Zhang

  4. College of Computer Science and Technology, Taiyuan University of Technology, Taiyuan, 030024, China

    Weili Wu

  5. Department of Computer Science, University of Texas at Dallas, Richardson, TX, 75080, USA

    Weili Wu

  6. Department of Mathematics, Ocean University of China, Qingdao, 266100, China

    Bin Liu

Authors
  1. Huijuan Wang
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  2. Lidong Wu
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  3. Xin Zhang
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  4. Weili Wu
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  5. Bin Liu
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Correspondence to Bin Liu.

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Wang, H., Wu, L., Zhang, X. et al. A note on the minimum number of choosability of planar graphs. J Comb Optim 31, 1013–1022 (2016). https://doi.org/10.1007/s10878-014-9805-2

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  • DOI: https://doi.org/10.1007/s10878-014-9805-2

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