Blocks of Hypergraphs applied to Hypergraphs and Outerplanarity

Ulrik Brandes (1) , Sabine Cornelsen (1) , Barbara Pampel (1) , Arnaud Sallaberry (2, 3, 4)

1 Department of Computer and Information Science, University of Konstanz
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique
3 GRAVITE - Graph Visualization and Interactive Exploration
4 PIKKO

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.

Domaines: Algorithme et structure de données [cs.DS]

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⟩