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Total coloring of graphs embedded in surfaces of nonnegative Euler characteristic

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Abstract

Let G be a graph which can be embedded in a surface of nonnegative Euler characteristic. In this paper, it is proved that the total chromatic number of G is Δ(G)+1 if Δ(G) ⩾ 9, where Δ(G) is the maximum degree of G.

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Authors and Affiliations

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

    HuiJuan Wang, JianLiang Wu & Bing Wang

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

    Bin Liu

  3. Department of Mathematics, Zaozhuang University, Zaozhuang, 277160, China

    Bing Wang

Authors
  1. HuiJuan Wang
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  2. Bin Liu
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  3. JianLiang Wu
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  4. Bing Wang
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Correspondence to Bin Liu.

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Wang, H., Liu, B., Wu, J. et al. Total coloring of graphs embedded in surfaces of nonnegative Euler characteristic. Sci. China Math. 57, 211–220 (2014). https://doi.org/10.1007/s11425-013-4576-2

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  • DOI: https://doi.org/10.1007/s11425-013-4576-2

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