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.

Source : oai:HAL:hal-01188904v1

Volume: Vol. 16 no. 3

Section: Graph Theory

Published on: September 25, 2014

Submitted on: June 30, 2013

Keywords: bicliques,bipartite graph,computational complexity,partitioning problem,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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