An Algorithmic Regularity Lemma for Hypergraphs
SIAM Journal on Computing
Extremal problems on set systems
Random Structures & Algorithms
The regularity lemma and its applications in graph theory
Theoretical aspects of computer science
Regularity properties for triple systems
Random Structures & Algorithms
Every monotone graph property is testable
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Linear equations, arithmetic progressions and hypergraph property testing
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
An Algorithmic Version of the Hypergraph Regularity Method
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Applications of the regularity lemma for uniform hypergraphs
Random Structures & Algorithms
The counting lemma for regular k-uniform hypergraphs
Random Structures & Algorithms
Arithmetic Progressions in Sets with Small Sumsets
Combinatorics, Probability and Computing
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
A new generalization of Mantel's theorem to k-graphs
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
Monochromatic Hamiltonian Berge-cycles in colored complete uniform hypergraphs
Journal of Combinatorial Theory Series B
The effect of induced subgraphs on quasi-randomness
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Hereditary properties of hypergraphs
Journal of Combinatorial Theory Series B
Green's conjecture and testing linear-invariant properties
Proceedings of the forty-first annual ACM symposium on Theory of computing
Weak hypergraph regularity and linear hypergraphs
Journal of Combinatorial Theory Series B
Hamilton ℓ-cycles in uniform hypergraphs
Journal of Combinatorial Theory Series A
The 3-colour ramsey number of a 3-uniform berge cycle
Combinatorics, Probability and Computing
Approximate Hypergraph Partitioning and Applications
SIAM Journal on Computing
Testing linear-invariant non-linear properties: a short report
Property testing
Green's conjecture and testing linear invariant properties
Property testing
Testing linear-invariant non-linear properties: a short report
Property testing
Green's conjecture and testing linear invariant properties
Property testing
Testing odd-cycle-freeness in Boolean functions
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Erdős-Hajnal-type theorems in hypergraphs
Journal of Combinatorial Theory Series B
Exact computation of the hypergraph Turán function for expanded complete 2-graphs
Journal of Combinatorial Theory Series B
Roth-type theorems in finite groups
European Journal of Combinatorics
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Szemerédi's Regularity Lemma proved to be a very powerful tool in extremal graph theory with a large number of applications. Chung [Regularity lemmas for hypergraphs and quasi-randomness, Random Structures Algorithms 2 (1991), 241-252], Frankl and Rödl [The uniformity lemma for hypergraphs, Graphs Combin 8 (1992), 309-312; Extremal problems on set systems, Random Structures Algorithms 20 (2002), 131-164] considered several extensions of Szemerédi's Regularity Lemma to hypergraphs. In particular, [Extremal problems on set systems, Random Structures Algorithms 20 (2002), 131-164] contains a regularity lemma for 3-uniform hypergraphs that was applied to a number of problems. In this paper, we present a generalization of this regularity lemma to k-uniform hypergraphs. Similar results were recently independently and alternatively obtained by W. T. Gowers.