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Universal Point Subsets for Planar Graphs

  • Patrizio Angelini
  • Carla Binucci
  • William Evans
  • Ferran Hurtado
  • Giuseppe Liotta
  • Tamara Mchedlidze
  • Henk Meijer
  • Yoshio Okamoto
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7676)

Abstract

A set S of k points in the plane is a universal point subset for a class \({\mathcal G}\) of planar graphs if every graph belonging to \({\mathcal G}\) admits a planar straight-line drawing such that k of its vertices are represented by the points of S. In this paper we study the following main problem: For a given class of graphs, what is the maximum k such that there exists a universal point subset of size k? We provide a [\({\sqrt{n} \;}\)] lower bound on k for the class of planar graphs with n vertices. In addition, we consider the value \(F(n, {\mathcal G})\) such that every set of \(F(n, {\mathcal G})\) points in general position is a universal subset for all graphs with n vertices belonging to the family \({\mathcal G}\), and we establish upper and lower bounds for \(F(n, {\mathcal G})\) for different families of planar graphs, including 4-connected planar graphs and nested-triangles graphs.

Keywords

Planar Graph General Position Maximal Chain Outer Face Geometric 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 2012

Authors and Affiliations

  • Patrizio Angelini
    • 1
  • Carla Binucci
    • 2
  • William Evans
    • 3
  • Ferran Hurtado
    • 4
  • Giuseppe Liotta
    • 2
  • Tamara Mchedlidze
    • 5
  • Henk Meijer
    • 6
  • Yoshio Okamoto
    • 7
  1. 1.Roma Tre UniversityItaly
  2. 2.University of PerugiaItaly
  3. 3.University of British ColumbiaCanada
  4. 4.Universitat Politécnica de CatalunyaSpain
  5. 5.Karlsruhe Institute of TechnologyGermany
  6. 6.Roosevelt AcademyNetherlands
  7. 7.University of Electro-CommunicationsJapan

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