On the generation of bicliques of a graph

  • Authors:

  • Vínia M. F. Dias;Celina M. H. de Figueiredo;Jayme L. Szwarcfiter

  • Affiliations:

  • COPPE, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, 21945-970 Rio de Janeiro, Brazil;IM and COPPE, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, 21945-970 Rio de Janeiro, Brazil;IM, COPPE, and NCE, Universidade Federal do Rio de Janeiro, Caixa Postal 68511, 21945-970 Rio de Janeiro, Brazil

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2007

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Abstract

An independent set of a graph is a subset of pairwise non-adjacentvertices. A complete bipartite set B is a subset of verticesadmitting a bipartition B=X∪Y, such that both X and Y areindependent sets, and all vertices of X are adjacent to those of Y.If both X,Y≠Ø, then B is called proper. A biclique is amaximal proper complete bipartite set of a graph. When therequirement that X and Y are independent sets of G is dropped, wehave a non-induced biclique. We show that it is NP-complete to testwhether a subset of the vertices of a graph is part of a biclique.We propose an algorithm that generates all non-induced bicliques ofa graph. In addition, we propose specialized efficient algorithmsfor generating the bicliques of special classes of graphs.