On planar supports for hypergraphs

K. Buchin, M.J. Kreveld, van, H. Meijer, B. Speckmann, K.A.B. Verbeek

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

13 Citations (Scopus)

Abstract

A graph G is a support for a hypergraph H=(V,S) if the vertices of G correspond to the vertices of H such that for each hyperedge Si e S the subgraph of G induced by Si 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.
Original languageEnglish
Title of host publicationGraph Drawing (17th International Symposium, GD'09, Chicago, IL, USA, September 22-25, 2009. Revised Papers)
EditorsD. Eppstein, E.R. Gansner
Place of PublicationBerlin
PublisherSpringer
Pages345-356
ISBN (Print)978-3-642-11804-3
DOIs
Publication statusPublished - 2010

Publication series

NameLecture Notes in Computer Science
Volume5849
ISSN (Print)0302-9743

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