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

• Autorzy: Xin Zhang , Guizhen Liu
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Independent crossing; IC-planar graph; Light edge; Coloring; Discharging

Kategorie tematyczne

• 05C15: Coloring of graphs and hypergraphs
• 05C10: Planar graphs; geometric and topological aspects of graph theory

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 2
• Strony: 308-321

Daty

wydano

2013-02-01

online

2012-11-21

Twórcy

autor

Xin Zhang

autor

Guizhen Liu

• Shandong University

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-012-0094-7