The minor crossing number of graphs with an excluded minor.

Bokal, Drago; Fijavz, Gasper; Wood, David R.

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Planar decompositions and the crossing number of graphs with an excluded minor.

Wood, David R., Telle, Jan Arne (2007)

The New York Journal of Mathematics [electronic only]

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Planarizing graphs---a survey and annotated bibliography.

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Crossing numbers and cutwidths.

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

Xin Zhang, Guizhen Liu (2013)

Open Mathematics

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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...