Geometric RAC simultaneous drawings of graphs

Argyriou, E; Bekos, M; Kaufmann, M; Symvonis, A

dc.contributor.author	Argyriou, E	en
dc.contributor.author	Bekos, M	en
dc.contributor.author	Kaufmann, M	en
dc.contributor.author	Symvonis, A	en
dc.date.accessioned	2014-03-01T02:53:38Z
dc.date.available	2014-03-01T02:53:38Z
dc.date.issued	2012	en
dc.identifier.issn	03029743	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/36465
dc.subject.other	Disjoint edges	en
dc.subject.other	Edge crossing	en
dc.subject.other	Embedded graphs	en
dc.subject.other	Input graphs	en
dc.subject.other	Linear time	en
dc.subject.other	Planar graph	en
dc.subject.other	Primal-dual	en
dc.subject.other	Straight-line drawings	en
dc.subject.other	Two-graphs	en
dc.subject.other	Vertex set	en
dc.subject.other	Geometry	en
dc.subject.other	Graphic methods	en
dc.subject.other	Graph theory	en
dc.title	Geometric RAC simultaneous drawings of graphs	en
heal.type	conferenceItem	en
heal.identifier.primary	10.1007/978-3-642-32241-9_25	en
heal.identifier.secondary	http://dx.doi.org/10.1007/978-3-642-32241-9_25	en
heal.publicationDate	2012	en
heal.abstract	In this paper, we study the geometric RAC simultaneous drawing problem: Given two planar graphs that share a common vertex set but have disjoint edge sets, a geometric RAC simultaneous drawing is a straight-line drawing in which (i) each graph is drawn planar, (ii) there are no edge overlaps, and, (iii) crossings between edges of the two graphs occur at right-angles. We first prove that two planar graphs admitting a geometric simultaneous drawing may not admit a geometric RAC simultaneous drawing. We further show that a cycle and a matching always admit a geometric RAC simultaneous drawing, which can be constructed in linear time. We also study a closely related problem according to which we are given a planar embedded graph G and the main goal is to determine a geometric drawing of G and its dual G* (without the face-vertex corresponding to the external face) such that: (i) G and G* are drawn planar, (ii) each vertex of the dual is drawn inside its corresponding face of G and, (iii) the primal-dual edge crossings form right-angles. We prove that it is always possible to construct such a drawing if the input graph is an outerplanar embedded graph. © 2012 Springer-Verlag.	en
heal.journalName	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)	en
dc.identifier.doi	10.1007/978-3-642-32241-9_25	en
dc.identifier.volume	7434 LNCS	en
dc.identifier.spage	287	en
dc.identifier.epage	298	en