Angelini, PatrizioBekos, Michael A.Katheder, JuliaKaufmann, MichaelPfister, MaximilianUeckerdt, Torsten2024-09-252024-09-252023Patrizio Angelini, Michael A. Bekos, Julia Katheder, Michael Kaufmann, Maximilian Pfister, and Torsten Ueckerdt. Axis-Parallel Right Angle Crossing Graphs. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs) 274(9):1-9:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)https://doi.org/10.4230/LIPIcs.ESA.2023.9https://hdl.handle.net/20.500.14490/334A 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.enAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/Graph drawingRAC graphsGraph drawing algorithmsBook chapter