Combining problems on RAC drawings and simultaneous graph drawings

  • Authors:

  • Evmorfia N. Argyriou;Michael A. Bekos;Michael Kaufmann;Antonios Symvonis

  • Affiliations:

  • School of Applied Mathematical & Physical Sciences, National Technical University of Athens, Greece;School of Applied Mathematical & Physical Sciences, National Technical University of Athens, Greece;Institute for Informatics, University of Tübingen, Germany;School of Applied Mathematical & Physical Sciences, National Technical University of Athens, Greece

  • Venue:
  • GD'11 Proceedings of the 19th international conference on Graph Drawing
  • Year:
  • 2011

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Abstract

We present an overview of the first combinatorial results for the so-called geometricRACsimultaneousdrawingproblem (or GRacSim drawing problem, for short), i.e., a combination of problems on geometric RAC drawings [3] and geometric simultaneous graph drawings [2]. According to this problem, we are given two planar graphs G1 =(V, E1 ) and G2 =(V, E2 ) that share a common vertex set but have disjoint edge sets, i.e., E1 ⊆V ×V , E2 ⊆V ×V and E1 ∩E2 =∅ The main task is to place the vertices on the plane so that, when the edges are drawn as straight-lines, (i) each graph is drawn planar, (ii) there are no edge overlaps, and, (iii) crossings between edges in E1 and E2 occur at right angles.