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

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Zhang X., Liu G.

Open Mathematics

2013

tom 11

nr 2

308-321

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.

Ograniczanie wyników

1 Open Mathematics

1 Liu G.

1 Zhang X.

1 2013

Wyniki wyszukiwania

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