1. Gap-planar Graphs
- Author
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Bae, Sang Won, Baffier, Jean-Francois, Chun, Jinhee, Eades, Peter, Eickmeyer, Kord, Grilli, Luca, Hong, Seok-Hee, Korman, Matias, Montecchiani, Fabrizio, Rutter, Ignaz, and Tóth, Csaba D.
- Subjects
Computer Science - Computational Geometry - Abstract
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., Comment: A preliminary version of this paper appeared in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017)
- Published
- 2017
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