Blocks of Hypergraphs applied to Hypergraphs and Outerplanarity
Résumé
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.
Origine : Fichiers produits par l'(les) auteur(s)
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