Complexity of minimum biclique cover and minimum biclique decomposition for bipartite domino-free graphs

33Citations
Citations of this article
17Readers
Mendeley users who have this article in their library.

Abstract

A biclique cover (resp. biclique decomposition) of a bipartite graph B is a family of complete bipartite subgraphs of B whose edges cover (resp. partition) the edges of B. The minimum cardinality of a biclique cover (resp. biclique decomposition) is denoted by s-dim(B) (resp. s-part(B)). The decision problems associated with the computation of s-dim and s-part are NP-complete for general bipartite graphs; the decision problem associated to s-dim is NP-complete for bipartite chordal graphs, and polynomial for bipartite distance-hereditary graphs, for bipartite convex graphs and for bipartite C4-free graphs. We show here that for bipartite domino-free graphs (a strict generalization of bipartite distance-hereditary graphs and bipartite C4-free graphs), s-dim and s-part are equal and can be computed in O(n × m) time. Moreover, we propose a O(n × m) time algorithm to check the domino-free property and to build the Galois lattice of such graphs. © 1998 Elsevier Science B.V. All rights reserved.

Cite

CITATION STYLE

APA

Amilhastre, J., Vilarem, M. C., & Janssen, P. (1998). Complexity of minimum biclique cover and minimum biclique decomposition for bipartite domino-free graphs. Discrete Applied Mathematics, 86(2–3), 125–144. https://doi.org/10.1016/S0166-218X(98)00039-0

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free