Journal of Graph Algorithms and Applications

Crossing Numbers of Beyond-Planar Graphs Revisited

Nathan van Beusekom, Irene Parada, and Bettina Speckmann

Vol. 26, no. 1, pp. 149-170, 2022. Regular paper.

Abstract Graph drawing beyond planarity focuses on drawings of high visual quality for non-planar graphs which are characterized by certain forbidden (edge) crossing 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.