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Algorithms for recognizing bipartite-Helly andbipartite-conformal hypergraphs*, **

Published online by Cambridge University Press:  24 October 2011

Marina Groshaus  and
Jayme Luis Szwarcfiter
Marina Groshaus
Affiliation:
Universidad de Buenos Aires, Departamento de Computación, CONICET Buenos Aires, Argentina. groshaus@dc.uba.ar
Jayme Luis Szwarcfiter
Affiliation:
Universidade Federal do Rio de Janeiro, IM, COPPE, and NCE, Rio de Janeiro, Brazil; jayme@nce.ufrj.br
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Abstract

A hypergraph is Helly if every family of hyperedges of it, formed by pairwiseintersecting hyperedges, has a common vertex. We consider the concepts ofbipartite-conformal and (colored) bipartite-Helly hypergraphs. In the same way asconformal hypergraphs and Helly hypergraphs are dual concepts, bipartite-conformal andbipartite-Helly hypergraphs are also dual. They are useful for characterizing bicliquematrices and biclique graphs, that is, the incident biclique-vertex incidence matrix andthe intersection graphs of the maximal bicliques of a graph, respectively. These conceptsplay 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 recognizingbipartite-conformal and bipartite-Helly hypergraphs as well as biclique matrices.

Keywords

Algorithmsbipartite graphsbiclique-Hellybiclique matricesclique matricesHelly propertyhypergraphs
Type
Research Article
Information
RAIRO - Operations Research , Volume 45 , Issue 3 , July 2011 , pp. 209 - 222
Copyright
© EDP Sciences, ROADEF, SMAI 2011

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