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Central European Journal of Mathematics

, Volume 11, Issue 2, pp 308–321 | Cite as

The structure of plane graphs with independent crossings and its applications to coloring problems

  • Xin ZhangEmail author
  • Guizhen Liu
Research Article

Abstract

If a graph G has a drawing in the plane in such a way that every two crossings are independent, then we call G a plane graph with independent crossings or IC-planar graph for short. In this paper, the structure of IC-planar graphs with minimum degree at least two or three is studied. By applying their structural results, we prove that the edge chromatic number of G is Δ if Δ ≥ 8, the list edge (resp. list total) chromatic number of G is Δ (resp. Δ + 1) if Δ ≥ 14 and the linear arboricity of G is ℈Δ/2⌊ if Δ ≥ 17, where G is an IC-planar graph and Δ is the maximum degree of G.

Keywords

Independent crossing IC-planar graph Light edge Coloring Discharging 

MSC

05C10 05C15 

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Copyright information

© Versita Warsaw and Springer-Verlag Wien 2012

Authors and Affiliations

  1. 1.Department of MathematicsXidian UniversityXi’anChina
  2. 2.School of MathematicsShandong UniversityJinanChina

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