Crossing Numbers of Beyond-Planar Graphs Revisited
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.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2021
- DOI:
- 10.48550/arXiv.2105.12452
- arXiv:
- arXiv:2105.12452
- Bibcode:
- 2021arXiv210512452V
- Keywords:
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- Computer Science - Computational Geometry