Plane Graphs with Maximum Degree 6 are Edge-face 8-colorable |
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| Authors: | Min Chen André Raspaud Weifan Wang |
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| Institution: | 1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China
2. LaBRI UMR CNRS 5800, Universite Bordeaux I, 33405, Talence Cedex, France
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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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