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.
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