On Universal Point Sets for Planar Graphs

  • Jean Cardinal
  • Michael Hoffmann
  • Vincent Kusters
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8296)

Abstract

A set P of points in ℝ2 is n-universal, if every planar graph on n vertices admits a plane straight-line embedding on P. Answering a question by Kobourov, we show that there is no n-universal point set of size n, for any n ≥ 15. Conversely, we use a computer program to show that there exist universal point sets for all n ≤ 10 and to enumerate all corresponding order types. Finally, we describe a collection \(\mathcal{G}\) of 7′393 planar graphs on 35 vertices that do not admit a simultaneous geometric embedding without mapping, that is, no set of 35 points in the plane supports a plane straight-line embedding of all graphs in \(\mathcal{G}\).

Keywords

Planar Graph Outer Face Construction Sequence Facial Triangle Maximal Planar 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 2013

Authors and Affiliations

  • Jean Cardinal
    • 1
  • Michael Hoffmann
    • 2
  • Vincent Kusters
    • 2
  1. 1.Département d’InformatiqueUniversité Libre de Bruxelles (ULB)Belgium
  2. 2.Institute of Theoretical Computer ScienceETH ZürichSwitzerland

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