The structure of plane graphs with independent crossings and its applications to coloring problems
نویسندگان
چکیده
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 ∆ if ∆ ≥ 8, the list edge (resp. list total) chromatic number of G is ∆ (resp. ∆ + 1) if ∆ ≥ 14 and the linear arboricity of G is d∆/2e if ∆ ≥ 17, where G is an IC-planar graph and ∆ is the maximum degree of G. MSC: 05C10, 05C15
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