Axis-Parallel Right Angle Crossing Graphs
Abstract
A RAC graph is one admitting a RAC drawing, that is, a polyline drawing in which each crossing occurs at a right angle. Originally motivated by psychological studies on readability of graph layouts, RAC graphs form one of the most prominent graph classes in beyond planarity. In this work, we study a subclass of RAC graphs, called axis-parallel RAC (or apRAC, for short), that restricts the crossings to pairs of axis-parallel edge-segments. apRAC drawings combine the readability of planar drawings with the clarity of (non-planar) orthogonal drawings. We consider these graphs both with and without bends. Our contribution is as follows: (i) We study inclusion relationships between apRAC and traditional RAC graphs. (ii) We establish bounds on the edge density of apRAC graphs. (iii) We show that every graph with maximum degree 8 is 2-bend apRAC and give a linear time drawing algorithm. Some of our results on apRAC graphs also improve the state of the art for general RAC graphs. We conclude our work with a list of open questions and a discussion of a natural generalization of the apRAC model.
Cite
@article{arxiv.2306.17073,
title = {Axis-Parallel Right Angle Crossing Graphs},
author = {Patrizio Angelini and Michael A. Bekos and Julia Katheder and Michael Kaufmann and Maximilian Pfister and Torsten Ueckerdt},
journal= {arXiv preprint arXiv:2306.17073},
year = {2023}
}