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Total coloring of embedded graphs of maximum degree at least ten

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Abstract

A total k-coloring of a graph G is a coloring of V(G) ∪ E(G) using k colors such that no two adjacent or incident elements receive the same color. The total chromatic number χ″(G) is the smallest integer k such that G has a total k-coloring. In this paper, it is proved that the total chromatic number of any graph G embedded in a surface Σ of Euler characteristic χ(Σ) ⩾ 0 is Δ(G) + 1 if Δ(G) ⩾ 10, where Δ(G) denotes the maximum degree of G.

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Authors and Affiliations

  1. Center for Discrete Mathematics, Fuzhou University, Fuzhou, 350002, China

    JianFeng Hou

  2. School of Mathematics, Shandong University, Jinan, 250100, China

    JianFeng Hou, JianLiang Wu, GuiZhen Liu & Bin Liu

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  1. JianFeng Hou
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  2. JianLiang Wu
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  3. GuiZhen Liu
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  4. Bin Liu
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Correspondence to JianLiang Wu.

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Hou, J., Wu, J., Liu, G. et al. Total coloring of embedded graphs of maximum degree at least ten. Sci. China Math. 53, 2127–2133 (2010). https://doi.org/10.1007/s11425-010-3089-5

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  • DOI: https://doi.org/10.1007/s11425-010-3089-5

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