Dias, V. M.; de Figueiredo, C. M. & Szwarcfiter, J. L.: Generating bicliques of a graph in lexicographic order. In:
Theoretical Computer Science 337 (2005), Nr. 1-3, S. 240 - 248
[Volltext]
[Kurzfassung]
[BibTeX]
An independent set of a graph is a subset of pairwise non-adjacent vertices. A complete bipartite set B is a subset of vertices admitting a bipartition B=X[union or logical sum]Y, such that both X and Y are independent sets, and all vertices of X are adjacent to those of Y. If both X,Y[not equal to][empty set], then B is called proper. A biclique is a maximal proper complete bipartite set of a graph. We present an algorithm that generates all bicliques of a graph in lexicographic order, with polynomial-time delay between the output of two successive bicliques. We also show that there is no polynomial-time delay algorithm for generating all bicliques in reverse lexicographic order, unless P=NP. The methods are based on those by Johnson, Papadimitriou and Yannakakis, in the solution of these two problems for independent sets, instead of bicliques.