Gap-planar Graphs

by   Sang Won Bae, et al.
National Institute of Informatics
The University of Sydney
Tohoku University
Universität Passau
Technische Universität Darmstadt
Università Perugia
California State University, Northridge

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.


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