Abstract
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 ∪ 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 ≠ ∅ , 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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
