Universal Point Sets for Drawing Planar Graphs with Circular Arcs

We prove that there exists a set S of n points in the plane such that every n-vertex planar graph G admits a planar drawing in which every vertex of G is placed on a distinct point of S and every edge of G is drawn as a circular arc. Submitted: October 2013 Reviewed: February 2014 Revised: March 2014 Accepted: April 2014 Final: May 2014 Published: May 2014 Article type: Regular paper Communicated by: Csaba D. Tóth An earlier version of this paper appeared as “Universal Point Sets for Planar Graph Drawings with Circular Arcs”, Proc. 25th Canadian Conf. Comput. Geom., pages 117–122, 2013. David Eppstein was supported in part by the National Science Foundation under grants 0830403 and 1217322, and by the Office of Naval Research under MURI grant N00014-08-11015. Patrizio Angelini, Michael Kaufmann, and Alexander Wolff acknowledge support by the ESF EuroGIGA project GraDR (DFG grants Ka 812/16-1 and Wo 758/5-1). E-mail address: [email protected] (Patrizio Angelini) [email protected] (David Eppstein) [email protected] (Fabrizio Frati) [email protected] (Michael Kaufmann) [email protected] (Sylvain Lazard) [email protected] (Tamara Mchedlidze) [email protected] (Monique Teillaud) WWW: http://www1.informatik.uni-wuerzburg.de/en/staff/wolff alexander (Alexander Wolff) 314 Angelini et al. Circular Arc Drawings