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Simultaneous Embedding of Embedded Planar Graphs

  • Patrizio Angelini
  • Giuseppe Di Battista
  • Fabrizio Frati
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7074)

Abstract

Given k planar graphs G 1,…,G k , deciding whether they admit a simultaneous embedding with fixed edges (Sefe ) and whether they admit a simultaneous geometric embedding (Sge ) are NP-hard problems, for k ≥ 3 and for k ≥ 2, respectively. In this paper we consider the complexity of Sefe and of Sge when the graphs G 1,…,G k have a fixed planar embedding. In sharp contrast with the NP-hardness of Sefe for three non-embedded graphs, we show that Sefe is polynomial-time solvable for three graphs with a fixed planar embedding. Furthermore, we show that, given k embedded planar graphs G 1,…,G k , deciding whether a Sefe of G 1,…,G k exists and deciding whether an Sge of G 1,…,G k exists are NP-hard problems, for k ≥ 14 and k ≥ 13, respectively.

Keywords

Planar Graph Hamiltonian Cycle Outer Face Simple Cycle Outerplanar Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Patrizio Angelini
    • 1
  • Giuseppe Di Battista
    • 1
  • Fabrizio Frati
    • 1
    • 2
  1. 1.Dipartimento di Informatica e AutomazioneUniversità Roma TreItaly
  2. 2.School of Information TechnologiesThe University of SydneyAustralia

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