Duginov, Oleg - Partitioning the vertex set of a bipartite graph into complete bipartite subgraphs

dmtcs:2090 - Discrete Mathematics & Theoretical Computer Science, September 25, 2014, Vol. 16 no. 3 (in progress)
Partitioning the vertex set of a bipartite graph into complete bipartite subgraphs

Authors: Duginov, Oleg

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 (in progress)
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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