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arXiv · 2105.12452

Crossing Numbers of Beyond-Planar Graphs Revisited

Nathan van Beusekom·Irene Parada·Bettina Speckmann
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Abstract

Graph drawing beyond planarity focuses on drawings of high visual quality for non-planar graphs which are characterized by certain forbidden edge configurations. A natural criterion for the quality of a drawing is the number of edge crossings. The question then arises whether beyond-planar drawings have a significantly larger crossing number than unrestricted drawings. Chimani et al. [GD'19] gave bounds for the ratio between the crossing number of three classes of beyond-planar graphs and the unrestricted crossing number. In this paper we extend their results to the main currently known classes of beyond-planar graphs characterized by forbidden edge configurations and answer several of their open questions.

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Nathan van Beusekom, Irene Parada, Bettina Speckmann. 2021-05-26. Crossing Numbers of Beyond-Planar Graphs Revisited. https://arxiv.org/abs/2105.12452

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