Gap-planar Graphs


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 finds motivation in edge casing, as a k-gapplanar 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.

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@article{Bae2017GapplanarG, title={Gap-planar Graphs}, author={Sang Won Bae and Jean-François Baffier and Jinhee Chun and Peter Eades and Kord Eickmeyer and Luca Grilli and Seok-Hee Hong and Matias Korman and Fabrizio Montecchiani and Ignaz Rutter and Csaba D. T{\'o}th}, journal={CoRR}, year={2017}, volume={abs/1708.07653} }