Biclique: an R package for maximal biclique enumeration in bipartite graphs
نویسندگان
چکیده
منابع مشابه
Hereditary biclique-Helly graphs: recognition and maximal biclique enumeration
A biclique is a set of vertices that induce a bipartite complete graph. A graph G is biclique-Helly when its family of maximal bicliques satisfies the Helly property. If every induced subgraph of G is also biclique-Helly, then G is hereditary biclique-Helly. A graph is C4-dominated when every cycle of length 4 contains a vertex that is dominated by the vertex of the cycle that is not adjacent t...
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A biclique of a graph G is a maximal induced complete bipartite subgraph of G. Given a graph G, the biclique matrix of G is a {0,1,−1} matrix having one row for each biclique and one column for each vertex of G, and such that a pair of 1, −1 entries in a same row corresponds exactly to adjacent vertices in the corresponding biclique. We describe a characterization of biclique matrices, in simil...
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Biclique-colouring is a colouring of the vertices of a graph in such a way that no maximal complete bipartite subgraph with at least one edge is monochromatic. We show that it is coNP-complete to check whether a given function that associates a colour to each vertex is a bicliquecolouring, a result that justifies the search for structured classes where the biclique-colouring problem could be ef...
متن کاملBiclique-Helly Graphs
A graph is biclique-Helly when its family of (maximal) bicliques is a Helly family. We describe characterizations for biclique-Helly graphs, leading to polynomial time recognition algorithms. In addition, we relate biclique-Helly graphs to the classes of clique-Helly, disk-Helly and neighborhood-Helly graphs.
متن کاملComplexity of minimum biclique decomposition of bipartite graphs
Many problems studied in graph theory are graph decomposition problems. The minimum number of complete bipartite graphs needed to partition the edges of a bipartite graph. is one of these problem and it is still open. We propose a NP-completness proof for its decision version and we show that it is polynomial on bipartite C4-free graphs.
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ژورنال
عنوان ژورنال: BMC Research Notes
سال: 2020
ISSN: 1756-0500
DOI: 10.1186/s13104-020-04955-0