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Blocks of Hypergraphs applied to Hypergraphs and Outerplanarity

Ulrik Brandes 1 Sabine Cornelsen 1 Barbara Pampel 1 Arnaud Sallaberry 2, 3, 4, *
* Corresponding author
3 GRAVITE - Graph Visualization and Interactive Exploration
Université Sciences et Technologies - Bordeaux 1, Inria Bordeaux - Sud-Ouest, École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), CNRS - Centre National de la Recherche Scientifique : UMR
Abstract : 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 NP-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 dierences 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 denition of biconnected components in hypergraphs.
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Ulrik Brandes, Sabine Cornelsen, Barbara Pampel, Arnaud Sallaberry. Blocks of Hypergraphs applied to Hypergraphs and Outerplanarity. 21st International Workshop on Combinatorial Algorithms (IWOCA 2010), Jul 2010, United Kingdom. pp.201-211. ⟨hal-00539143⟩

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