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arXiv · 1908.03153

Crossing Numbers of Beyond-Planar Graphs

Markus Chimani·Philipp Kindermann·Fabrizio Montecchiani·Pavel Valtr
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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.

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Markus Chimani, Philipp Kindermann, Fabrizio Montecchiani, Pavel Valtr. 2019-08-08. Crossing Numbers of Beyond-Planar Graphs. https://arxiv.org/abs/1908.03153

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