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arXiv · 1708.07653

Gap-planar Graphs

Sang Won Bae·Jean-Francois Baffier·Jinhee Chun·Peter Eades·Kord Eickmeyer·Luca Grilli·Seok-Hee Hong·Matias Korman·Fabrizio Montecchiani·Ignaz Rutter·Csaba D. Tóth
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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.

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Sang Won Bae, Jean-Francois Baffier, Jinhee Chun, Peter Eades, Kord Eickmeyer, Luca Grilli, Seok-Hee Hong, Matias Korman, Fabrizio Montecchiani, Ignaz Rutter, Csaba D. Tóth. 2017-08-25. Gap-planar Graphs. https://doi.org/10.1016/j.tcs.2018.05.031

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