Blocks of Hypergraphs

Applied to Hypergraphs and Outerplanarity
  • Ulrik Brandes
  • Sabine Cornelsen
  • Barbara Pampel
  • Arnaud Sallaberry
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6460)


A support of a hypergraph H is a graph with the same vertex set as H in which each hyperedge induces a connected subgraph. We show how to test in polynomial time whether a given hypergraph has a cactus support, i.e. a support that is a tree of edges and cycles. While it is \(\mathcal N\mathcal P\)-complete to decide whether a hypergraph has a 2-outerplanar support, we show how to test in polynomial time whether a hypergraph that is closed under intersections and differences has an outerplanar or a planar support. In all cases our algorithms yield a construction of the required support if it exists. The algorithms are based on a new definition of biconnected components in hypergraphs.


Bipartite Graph Planar Support Connected Subgraph Outer Face Hasse Diagram 
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 2011

Authors and Affiliations

  • Ulrik Brandes
    • 1
  • Sabine Cornelsen
    • 1
  • Barbara Pampel
    • 1
  • Arnaud Sallaberry
    • 2
  1. 1.Fachbereich Informatik & InformationswissenschaftUniversität KonstanzGermany
  2. 2.CNRS UMR 5800 LaBRIINRIA Bordeaux - Sud OuestPikkoFrance

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