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Generating bicliques of a graph in lexicographic order. (English) Zbl 1076.68048
A complete bipartite set $$B$$ of a graph is a subset of vertices admitting a bipartition $$B=X\cup Y$$ such that both $$X$$ and $$Y$$ are independent sets and all vertices of $$X$$ are adjacent to those of $$Y$$. If both $$X,Y\neq \emptyset$$, then $$B$$ is called proper. A biclique is a maximal proper complete bipartite set of a graph. The authors present an algorithm that generates all bicliques of a graph in lexicographic order, with polynomial-time delay between the output of two successive bicliques. They show also that there is no polynomial-time delay algorithm for generating all bicliques in reverse lexicographic order, unless P=NP. The paper contains an extension of results of D. S. Johnson, C. H. Papadimitriou and M. Yannakakis [“On generating all maximal independent sets”, Inf. Process. Lett. 27, 119–123 (1988; Zbl 0654.68086)].

MSC:
 68R10 Graph theory (including graph drawing) in computer science 05C85 Graph algorithms (graph-theoretic aspects) 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) 68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) 68Q25 Analysis of algorithms and problem complexity
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