On generating all maximal independent sets
Information Processing Letters
The number of maximal independent sets in triangle-free graphs
SIAM Journal on Discrete Mathematics
Discrete Applied Mathematics
Approximating clique and biclique problems
Journal of Algorithms
A fast algorithm for building lattices
Information Processing Letters
On bipartite and multipartite clique problems
Journal of Algorithms
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
Node-and edge-deletion NP-complete problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
The maximum edge biclique problem is NP-complete
Discrete Applied Mathematics
Consensus algorithms for the generation of all maximal bicliques
Discrete Applied Mathematics - The fourth international colloquium on graphs and optimisation (GO-IV)
Generating bicliques of a graph in lexicographic order
Theoretical Computer Science
Measure and conquer: a simple O(20.288n) independent set algorithm
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
On the generation of bicliques of a graph
Discrete Applied Mathematics
On the Minimum Feedback Vertex Set Problem: Exact and Enumeration Algorithms
Algorithmica - Parameterized and Exact Algorithms
A tighter bound for counting max-weight solutions to 2SAT instances
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
A branch-and-reduce algorithm for finding a minimum independent dominating set in graphs
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Measure and conquer: domination – a case study
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Linear-time counting algorithms for independent sets in chordal graphs
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Feedback vertex sets in tournaments
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Exact exponential-time algorithms for finding bicliques
Information Processing Letters
Covering and packing in linear space
Information Processing Letters
Exact algorithm for the maximum induced planar subgraph problem
ESA'11 Proceedings of the 19th European conference on Algorithms
Bicolored independent sets and bicliques
Information Processing Letters
Counting maximal independent sets in subcubic graphs
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
Feedback Vertex Sets in Tournaments
Journal of Graph Theory
Finding a maximum induced degenerate subgraph faster than 2n
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
A convexity upper bound for the number of maximal bicliques of a bipartite graph
Discrete Applied Mathematics
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Bicliques of graphs have been studied extensively, partially motivated by the large number of applications. One of the main algorithmic interests is in designing algorithms to enumerate all maximal bicliques of a (bipartite) graph. Polynomial-time reductions have been used explicitly or implicitly to design polynomial delay algorithms to enumerate all maximal bicliques. Based on polynomial-time Turing reductions, various algorithmic problems on (maximal) bicliques can be studied by considering the related problem for (maximal) independent sets. In this line of research, we improve Prisner's upper bound on the number of maximal bicliques [Combinatorica, 2000] and show that the maximum number of maximal bicliques in a graph on n vertices is exactly 3 n /3 (up to a polynomial factor). The main results of this paper are O (1.3642 n ) time algorithms to compute the number of maximal independent sets and maximal bicliques in a graph.