We introduce the family of k-gap-planar graphs for k \geq 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 finds motivation in edge casing, as a k-gap-planar graph can be drawn crossing-free after introducing at most k local gaps per edge. We obtain results on the maximum density , drawability of complete graphs, complexity of the recognition problem, and relationships with other families of beyond-planar graphs.
We introduce the family of k-gap-planar graphs for k \geq 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.
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finds motivation
is motivated by applications
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, drawability of complete graphs, complexity of the recognition problem, and relationships with other families of beyond-planar
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