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.
@article{bwmeta1.element.doi-10_2478_s11533-012-0094-7,
author = {Xin Zhang and Guizhen Liu},
title = {The structure of plane graphs with independent crossings and its applications to coloring problems},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {308-321},
zbl = {1258.05028},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0094-7}
}
Xin Zhang; Guizhen Liu. The structure of plane graphs with independent crossings and its applications to coloring problems. Open Mathematics, Tome 11 (2013) pp. 308-321. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0094-7/
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