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

Open Mathematics (2013)

• Volume: 11, Issue: 2, page 308-321
• ISSN: 2391-5455

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## Abstract

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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.

## How to cite

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Xin Zhang, and Guizhen Liu. "The structure of plane graphs with independent crossings and its applications to coloring problems." Open Mathematics 11.2 (2013): 308-321. <http://eudml.org/doc/269573>.

@article{XinZhang2013,
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.},
author = {Xin Zhang, Guizhen Liu},
journal = {Open Mathematics},
keywords = {Independent crossing; IC-planar graph; Light edge; Coloring; Discharging; independent crossing; independent crossing planar graph; light edge; coloring; discharging},
language = {eng},
number = {2},
pages = {308-321},
title = {The structure of plane graphs with independent crossings and its applications to coloring problems},
url = {http://eudml.org/doc/269573},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Xin Zhang
AU - Guizhen Liu
TI - The structure of plane graphs with independent crossings and its applications to coloring problems
JO - Open Mathematics
PY - 2013
VL - 11
IS - 2
SP - 308
EP - 321
AB - 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.
LA - eng
KW - Independent crossing; IC-planar graph; Light edge; Coloring; Discharging; independent crossing; independent crossing planar graph; light edge; coloring; discharging
UR - http://eudml.org/doc/269573
ER -

## References

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