Partitioning the vertex set of a bipartite graph into complete bipartite subgraphs

Oleg Duginov (1, 2)

1 Department of Combinatorial Models and Algorithms [Minsk]
2 NASB - National Academy of Sciences of Belarus

Given a graph and a positive integer k, the biclique vertex-partition problem asks whether the vertex set of the graph can be partitioned into at most k bicliques (connected complete bipartite subgraphs). It is known that this problem is NP-complete for bipartite graphs. In this paper we investigate the computational complexity of this problem in special subclasses of bipartite graphs. We prove that the biclique vertex-partition problem is polynomially solvable for bipartite permutation graphs, bipartite distance-hereditary graphs and remains NP-complete for perfect elimination bipartite graphs and bipartite graphs containing no 4-cycles as induced subgraphs.

Mots clés: bicliques; bipartite graph; computational complexity; partitioning problem

Domaines: Mathématique discrète [cs.DM]

Oleg Duginov. Partitioning the vertex set of a bipartite graph into complete bipartite subgraphs. Discrete Mathematics and Theoretical Computer Science, 2014, Vol. 16 no. 3 (3), pp.203--214. ⟨10.46298/dmtcs.2090⟩. ⟨hal-01188904⟩