Dense expanders and pseudo-random bipartite graphs
Discrete Mathematics
Graph decomposition is NPC - a complete proof of Holyer's conjecture
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
The algorithmic aspects of the regularity lemma
Journal of Algorithms
A Fast Approximation Algorithm for Computing theFrequencies of Subgraphs in a Given Graph
SIAM Journal on Computing
Ramsey properties of random hypergraphs
Journal of Combinatorial Theory Series A
Hypergraphs, quasi-randomness, and conditions for regularity
Journal of Combinatorial Theory Series A
An Algorithmic Regularity Lemma for Hypergraphs
SIAM Journal on Computing
Extremal problems on set systems
Random Structures & Algorithms
Efficient Testing of Hypergraphs
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
On characterizing hypergraph regularity
Random Structures & Algorithms - Special issue: Proceedings of the tenth international conference "Random structures and algorithms"
Integer and fractional packings in dense 3-uniform hypergraphs
Random Structures & Algorithms
The regularity lemma and approximation schemes for dense problems
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Regularity properties for triple systems
Random Structures & Algorithms
Hereditary Properties of Triple Systems
Combinatorics, Probability and Computing
A Note on a Question of Erdös and Graham
Combinatorics, Probability and Computing
Regularity lemma for k-uniform hypergraphs
Random Structures & Algorithms
Quasirandomness, Counting and Regularity for 3-Uniform Hypergraphs
Combinatorics, Probability and Computing
Applications of the regularity lemma for uniform hypergraphs
Random Structures & Algorithms
The counting lemma for regular k-uniform hypergraphs
Random Structures & Algorithms
The algorithmic aspects of the regularity lemma
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
A Dirac-Type Theorem for 3-Uniform Hypergraphs
Combinatorics, Probability and Computing
The counting lemma for regular k-uniform hypergraphs
Random Structures & Algorithms
Loose Hamilton cycles in 3-uniform hypergraphs of high minimum degree
Journal of Combinatorial Theory Series B
Integer and fractional packings of hypergraphs
Journal of Combinatorial Theory Series B
Property testing in hypergraphs and the removal lemma
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Hereditary properties of hypergraphs
Journal of Combinatorial Theory Series B
Hypergraph regularity and quasi-randomness
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
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Extending the Szemerédi Regularity Lemma for graphs, P. Frankl and the third author [11] established a 3-graph Regularity Lemma guaranteeing that all large triple systems admit partitions of their edge sets into constantlymany classes where most classes consist of regularly distributed edges. Many applications of this lemma require a companion Counting Lemma [26] allowing one to estimate the number of copies of K_k ^{(3)} in a "dense and regular" environment created by the 3-graph Regularity Lemma. Combined applications of these lemmas are known as the 3- graph Regularity Method. In this paper, we provide an algorithmic version of the 3-graph Regularity Lemma which, as we show, is compatible with a Counting Lemma. We also discuss some applications. For general k-uniform hypergraphs, Regularity and Counting Lemmas were recently established by Gowers [16] and by Nagle, R篓odl, Schacht, and Skokan [27, 35]. We believe the arguments here provide a basis toward a general algorithmic hypergraph regularity method.