COCOON 2012: Computing and Combinatorics pp 287-298

Geometric RAC Simultaneous Drawings of Graphs

• Evmorfia Argyriou
• Michael Bekos
• Michael Kaufmann
• Antonios Symvonis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7434)

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.

Meijer

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Authors and Affiliations

• Evmorfia Argyriou
• 1
• Michael Bekos
• 2
• Michael Kaufmann
• 2
• Antonios Symvonis
• 1
1. 1.School of Applied Mathematical & Physical SciencesNational Technical University of AthensGreece
2. 2.Institute for InformaticsUniversity of TübingenGermany