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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.

Keywords

Tree Support Total Demand Connectivity Structure Dual Graph Planar Support 
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 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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