Volume 45, Number 3, July-September 2011
|Page(s)||209 - 222|
|Published online||24 October 2011|
Universidad de Buenos Aires, Departamento de
Computación, CONICET Buenos
2 Universidade Federal do Rio de Janeiro, IM, COPPE, and NCE, Rio de Janeiro, Brazil
Accepted: 19 July 2011
A hypergraph is Helly if every family of hyperedges of it, formed by pairwise intersecting hyperedges, has a common vertex. We consider the concepts of bipartite-conformal and (colored) bipartite-Helly hypergraphs. In the same way as conformal hypergraphs and Helly hypergraphs are dual concepts, bipartite-conformal and bipartite-Helly hypergraphs are also dual. They are useful for characterizing biclique matrices and biclique graphs, that is, the incident biclique-vertex incidence matrix and the intersection graphs of the maximal bicliques of a graph, respectively. These concepts play a similar role for the bicliques of a graph, as do clique matrices and clique graphs, for the cliques of the graph. We describe polynomial time algorithms for recognizing bipartite-conformal and bipartite-Helly hypergraphs as well as biclique matrices.
Mathematics Subject Classification: 05C85 / 68505
Key words: Algorithms / bipartite graphs / biclique-Helly / biclique matrices / clique matrices / Helly property / hypergraphs
© EDP Sciences, ROADEF, SMAI 2011
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