# complete bipartite graph

(redirected from Biclique)

## complete bipartite graph

[kəm¦plēt bī′pär‚tīt ‚graf]
(mathematics)
A graph whose vertices can be partitioned into two sets such that every edge joins a vertex in one set with a vertex in the other, and each vertex in one set is joined to each vertex in the other by exactly one edge.
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Biclique algorithm was recruited from the website of the Computational Biology Laboratory in the Department of Computer Science, Iowa State University (http:// genome.
In order to extract synergistic, competing lncRNA modules, the Biclique algorithm was used in this study.
V(D) with supremum u is associated with a reduced biclique V[right arrow]W such that V = {out(v) | v[right arrow]u [member of] E(D)} and W = {in(w) | u[right arrow]w [member of] E(D)}.
Moreover, each A [subset or equal to] V(D) with supremum u is associated with a reduced biclique V [right arrow] W such that V = {out(v) | v [right arrow] u [member of] E(D)} and W = {in(w) | u [right arrow] w [member of] E(D)}.
Then the biclique cryptanalysis of the TWINE has been proposed in [11-12].
1: A biclique C = (S', A') is a subgraph of G induced by a pair of two disjoint subsets S' [subset or equal to] S, A' [subset or equal to] A, such that [for all]s [member of] S', a [member of] A, (s, a) [member of] E, meaning that a biclique in a bipartite graph is a complete bipartite subgraph that contains all permissible edges.
2: A maximum biclique is a largest biclique in a bipartite graph.
A graph is biclique-Helly when its family of maximal bicliques is Helly.
Furthermore, we prove that every maximal biclique of a graph in this class is formed by those vertices that either are adjacent or dominate v, for some vertex v.
In this paper, we establish the relationship between this concept and biclique cover.
In graph theory, the Helly property has been applied to families of sets, such as cliques, disks, bicliques, and neighbourhoods, leading to the classes of clique-Helly, disk-Helly, biclique-Helly, neighbourhood-Helly graphs, respectively.
Liedloff, On Independent Sets and Bicliques in Graphs, Algorithmica, 62, (2012), pp.

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