Drawing Graphs with Circular Arcs and Right-Angle Crossings

Steven Chaplick, Henry Förster, Myroslav Kryven, Alexander Wolff

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review


In a RAC drawing of a graph, vertices are represented by points in the plane, adjacent vertices are connected by line segments, and crossings must form right angles. Graphs that admit such drawings are RAC graphs. RAC graphs are beyond-planar graphs and have been studied extensively. In particular, it is known that a RAC graph with n vertices has at most 4n − 10 edges. We introduce a superclass of RAC graphs, which we call arc-RAC graphs. A graph is arc-RAC if it admits a drawing where edges are represented by circular arcs and crossings form right angles. We provide a Turán-type result showing that an arc-RAC graph with n vertices has at most 14n − 12 edges and that there are n-vertex arc-RAC graphs with 4.5n − O(√n) edges.

Original languageEnglish
Title of host publication17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)
EditorsSusanne Albers
Publication statusPublished - 2020

Publication series

SeriesLeibniz International Proceedings in Informatics

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