On co-bicliques
RAIRO - Operations Research - Recherche Opérationnelle, Tome 41 (2007) no. 3, pp. 295-304.

A co-biclique of a simple undirected graph G=(V,E) is the edge-set of two disjoint complete subgraphs of G. (A co-biclique is the complement of a biclique.) A subset FE is an independent of G if there is a co-biclique B such that FB, otherwise F is a dependent of G. This paper describes the minimal dependents of G. (A minimal dependent is a dependent C such that any proper subset of C is an independent.) It is showed that a minimum-cost dependent set of G can be determined in polynomial time for any nonnegative cost vector x + E . Based on this, we obtain a branch-and-cut algorithm for the maximum co-biclique problem which is, given a weight vector w + E , to find a co-biclique B of G maximizing w(B)= eB w e .

DOI : 10.1051/ro:2007020
Classification : 05C15, 90C09
Mots clés : co-bicyclique, signed graph, branch-and-cut
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Cornaz, Denis. On co-bicliques. RAIRO - Operations Research - Recherche Opérationnelle, Tome 41 (2007) no. 3, pp. 295-304. doi : 10.1051/ro:2007020. http://archive.numdam.org/articles/10.1051/ro:2007020/

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