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List edge and list total coloring of 1-planar graphs

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Abstract

A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, it is proved that each 1-planar graph with maximum degree Δ is (Δ+1)-edge-choosable and (Δ+2)-total-choosable if Δ ⩾ 16, and is Δ-edge-choosable and (Δ+1)-total-choosable if Δ ⩾ 21. The second conclusion confirms the list coloring conjecture for the class of 1-planar graphs with large maximum degree.

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Authors and Affiliations

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

    Xin Zhang, Jianliang Wu & Guizhen Liu

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  1. Xin Zhang
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  2. Jianliang Wu
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  3. Guizhen Liu
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Correspondence to Guizhen Liu.

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Zhang, X., Wu, J. & Liu, G. List edge and list total coloring of 1-planar graphs. Front. Math. China 7, 1005–1018 (2012). https://doi.org/10.1007/s11464-012-0184-7

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  • DOI: https://doi.org/10.1007/s11464-012-0184-7

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