Crossing Numbers of Beyond-Planar Graphs

08/08/2019

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by   Markus Chimani, et al.

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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 Ω(n) crossings, while O(1) crossings suffice in a crossing-minimal drawing without restrictions on local edge crossing patterns.