Crossing Numbers of Beyond-Planar Graphs

Markus Chimani; Philipp Kindermann; Fabrizio Montecchiani; Pavel Valtr

Crossing Numbers of Beyond-Planar Graphs

Computational Geometry 2019-09-10 v2 Discrete Mathematics

Authors: Markus Chimani , Philipp Kindermann , Fabrizio Montecchiani , Pavel Valtr

Abstract

We study the 1-planar, quasi-planar, and fan-planar crossing number in comparison to the (unrestricted) crossing number of graphs. We prove that there are $n$ -vertex 1-planar (quasi-planar, fan-planar) graphs such that any 1-planar (quasi-planar, fan-planar) drawing has $\Omega(n)$ crossings, while $O(1)$ crossings suffice in a crossing-minimal drawing without restrictions on local edge crossing patterns.

Keywords

planar graph drawing graph theory

Cite

@article{arxiv.1908.03153,
  title  = {Crossing Numbers of Beyond-Planar Graphs},
  author = {Markus Chimani and Philipp Kindermann and Fabrizio Montecchiani and Pavel Valtr},
  journal= {arXiv preprint arXiv:1908.03153},
  year   = {2019}
}

Comments

Appears in the Proceedings of the 27th International Symposium on Graph Drawing and Network Visualization (GD 2019)

Crossing Numbers of Beyond-Planar Graphs

Abstract

Keywords

Cite

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