Gap-planar Graphs

08/25/2017

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by   Sang Won Bae, et al.

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We introduce the family of k-gap-planar graphs for k ≥ 0, i.e., graphs that have a drawing in which each crossing is assigned to one of the two involved edges and each edge is assigned at most k of its crossings. This definition is motivated by applications in edge casing, as a k-gap-planar graph can be drawn crossing-free after introducing at most k local gaps per edge. We present results on the maximum density of k-gap-planar graphs, their relationship to other classes of beyond-planar graphs, characterization of k-gap-planar complete graphs, and the computational complexity of recognizing k-gap-planar graphs.