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.
@InProceedings{angelini_et_al:LIPIcs.ESA.2023.9, author = {Angelini, Patrizio and Bekos, Michael A. and Katheder, Julia and Kaufmann, Michael and Pfister, Maximilian and Ueckerdt, Torsten}, title = {{Axis-Parallel Right Angle Crossing Graphs}}, booktitle = {31st Annual European Symposium on Algorithms (ESA 2023)}, pages = {9:1--9:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-295-2}, ISSN = {1868-8969}, year = {2023}, volume = {274}, editor = {G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.9}, URN = {urn:nbn:de:0030-drops-186623}, doi = {10.4230/LIPIcs.ESA.2023.9}, annote = {Keywords: Graph drawing, RAC graphs, Graph drawing algorithms} }
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