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Plane Graphs with Maximum Degree 6 are Edge-face 8-colorable

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Abstract

A plane graph G is edge-face k-colorable if the elements of \({E(G) \cup F(G)}\) can be colored with k colors so that any two adjacent or incident elements receive different colors. Sanders and Zhao conjectured that every plane graph with maximum degree Δ is edge-face (Δ +  2)-colorable and left the cases \({\Delta \in \{4, 5, 6\}}\) unsolved. In this paper, we settle the case Δ =  6. More precisely, we prove that every plane graph with maximum degree 6 is edge-face 8-colorable.

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Authors and Affiliations

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

    Min Chen & Weifan Wang

  2. LaBRI UMR CNRS 5800, Universite Bordeaux I, 33405, Talence Cedex, France

    André Raspaud

Authors
  1. Min Chen
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  2. André Raspaud
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  3. Weifan Wang
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Correspondence to Min Chen.

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Chen, M., Raspaud, A. & Wang, W. Plane Graphs with Maximum Degree 6 are Edge-face 8-colorable. Graphs and Combinatorics 30, 861–874 (2014). https://doi.org/10.1007/s00373-013-1308-x

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  • DOI: https://doi.org/10.1007/s00373-013-1308-x

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