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Equitable Coloring of Three Classes of 1-planar Graphs

  • Xin ZhangEmail author
  • Hui-juan Wang
  • Lan Xu
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Abstract

A graph is 1-planar if it can be drawn on a plane so that each edge is crossed by at most one other edge. A plane graph with near-independent crossings or independent crossings, say NIC-planar graph or IC-planar graph, is a 1-planar graph with the restriction that for any two crossings the four crossed edges are incident with at most one common vertex or no common vertices, respectively. In this paper, we prove that each 1-planar graph, NIC-planar graph or IC-planar graph with maximum degree Δ at least 15, 13 or 12 has an equitable Δ-coloring, respectively. This verifies the well-known Chen-Lih-Wu Conjecture for three classes of 1-planar graphs and improves some known results.

Keywords

1-planar graph equitable coloring independent crossing 

2000 MR Subject Classification

05C15 05C10 

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Copyright information

© Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsXidian UniversityXi’anChina
  2. 2.College of MathematicsQingdao UniversityQingdaoChina
  3. 3.Department of MathematicsChangji UniversityChangjiChina

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