Geometric RAC Simultaneous Drawings of Graphs

  • Evmorfia Argyriou
  • Michael Bekos
  • Michael Kaufmann
  • Antonios Symvonis
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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

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

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