Generating bicliques of a graph in lexicographic order
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Theoretical Computer Science 337 (1-3): 240 - 248 (2005)

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=Xunion or logical sumY, such that both X and Y are independent sets, and all vertices of X are adjacent to those of Y. If both X,Ynot equal toempty 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.
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