| Issue |
RAIRO-Oper. Res.
Volume 41, Number 3, July-September 2007
Journées Polyèdres et Optimisation Combinatoire
|
|
|---|---|---|
| Page(s) | 295 - 304 | |
| DOI | https://doi.org/10.1051/ro:2007020 | |
| Published online | 21 August 2007 | |
On co-bicliques
Équipe Combinatoire, UFR 921, Case 189,
Université Pierre et Marie Curie, 4 place Jussieu, 75252 Paris
Cedex 05 France; cornaz@math.jussieu.fr
Received:
4
December
2006
Accepted:
21
December
2006
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 F ⊆ E is an independent of G if there is a co-biclique B such that F ⊆ B, 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 
. Based on this, we obtain a branch-and-cut algorithm for the maximum co-biclique problem which is, given a weight vector 
, to find a co-biclique B of G maximizing w(B) = ∑e∈B we.
Mathematics Subject Classification: 05C15 / 90C09
Key words: Co-bicyclique / signed graph / branch-and-cut
© EDP Sciences, ROADEF, SMAI, 2007
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