Crossing Numbers of Beyond-Planar Graphs Revisited

TL;DR

This paper investigates the crossing numbers of beyond-planar graphs, extending previous bounds and answering open questions to better understand their visual complexity compared to unrestricted graphs.

Contribution

It extends existing bounds on crossing numbers to main classes of beyond-planar graphs and addresses open questions in the field.

Findings

Extended bounds for crossing numbers of beyond-planar graphs.

Answered several open questions from prior research.

Provided insights into the visual complexity of beyond-planar graph drawings.

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.