Arboricity and bipartite subgraph listing algorithms
Information Processing Letters
Formal Concept Analysis: Mathematical Foundations
Formal Concept Analysis: Mathematical Foundations
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Linear algorithms to recognize interval graphs and test for the consecutive ones property
STOC '75 Proceedings of seventh annual ACM symposium on Theory of computing
The maximum edge biclique problem is NP-complete
Discrete Applied Mathematics
A Linear Delay Algorithm for Building Concept Lattices
CPM '08 Proceedings of the 19th annual symposium on Combinatorial Pattern Matching
On Independent Sets and Bicliques in Graphs
Graph-Theoretic Concepts in Computer Science
Exact exponential-time algorithms for finding bicliques
Information Processing Letters
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Given a bipartite graph, we present an upper bound for its number of maximal bicliques as the product of the numbers of maximal bicliques of two appropriate subgraphs. Such an upper bound is a function of bipartite convexity, a generalization of the convex property for bipartite graphs. We survey known upper bounds present in the literature and construct families of graphs for which our bound is sharper than all the other known bounds. For particular families, only our upper bound is polynomial. We also show that determining convexity is NP-hard.