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Frontiers of Mathematics in China

, Volume 7, Issue 5, pp 1005–1018 | Cite as

List edge and list total coloring of 1-planar graphs

  • Xin Zhang
  • Jianliang Wu
  • Guizhen LiuEmail author
Research Article

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.

Keywords

1-planar graph list coloring conjecture discharging 

MSC

05C10 05C15 

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Copyright information

© Higher Education Press and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.School of MathematicsShandong UniversityJinanChina

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