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 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. © 2011 Springer-Verlag.
CITATION STYLE
Brandes, U., Cornelsen, S., Pampel, B., & Sallaberry, A. (2011). Blocks of hypergraphs: Applied to hypergraphs and outerplanarity. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6460 LNCS, pp. 201–211). https://doi.org/10.1007/978-3-642-19222-7_21
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