On Planar Supports for Hypergraphs

  • Kevin Buchin
  • Marc van Kreveld
  • Henk Meijer
  • Bettina Speckmann
  • Kevin Verbeek
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5849)

Abstract

A graph G is a support for a hypergraph \(H = (V, \mathcal{S})\) if the vertices of G correspond to the vertices of H such that for each hyperedge \(S_i \in \mathcal{S}\) the subgraph of G induced by S i is connected. G is a planar support if it is a support and planar. Johnson and Pollak [9] proved that it is NP-complete to decide if a given hypergraph has a planar support. In contrast, there are polynomial time algorithms to test whether a given hypergraph has a planar support that is a path, cycle, or tree. In this paper we present an algorithm which tests in polynomial time if a given hypergraph has a planar support that is a tree where the maximal degree of each vertex is bounded. Our algorithm is constructive and computes a support if it exists. Furthermore, we prove that it is already NP-hard to decide if a hypergraph has a 3-outerplanar support.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Kevin Buchin
    • 1
  • Marc van Kreveld
    • 2
  • Henk Meijer
    • 3
  • Bettina Speckmann
    • 1
  • Kevin Verbeek
    • 1
  1. 1.Dep. of Mathematics and Computer ScienceTU EindhovenThe Netherlands
  2. 2.Dep. of Computer ScienceUtrecht UniversityThe Netherlands
  3. 3.Roosevelt AcademyMiddelburgThe Netherlands

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