Journal of Combinatorial Theory Series A
Extremal problems on set systems
Random Structures & Algorithms
A Note on a Question of Erdös and Graham
Combinatorics, Probability and Computing
The counting lemma for regular k-uniform hypergraphs
Random Structures & Algorithms
An Algorithmic Version of the Hypergraph Regularity Method
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
The counting lemma for regular k-uniform hypergraphs
Random Structures & Algorithms
Product growth and mixing in finite groups
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
The effect of induced subgraphs on quasi-randomness
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
3-Uniform hypergraphs of bounded degree have linear Ramsey numbers
Journal of Combinatorial Theory Series B
Combinatorics, Probability and 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
Green's conjecture and testing linear-invariant properties
Proceedings of the forty-first annual ACM symposium on Theory of computing
Combinatorial Problems for Horn Clauses
Graph Theory, Computational Intelligence and Thought
Weak hypergraph regularity and linear hypergraphs
Journal of Combinatorial Theory Series B
Green's conjecture and testing linear invariant properties
Property testing
Green's conjecture and testing linear invariant properties
Property testing
A deterministic algorithm for the Frieze-Kannan regularity lemma
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
On laplacians of random complexes
Proceedings of the twenty-eighth annual symposium on Computational geometry
A Deterministic Algorithm for the Frieze-Kannan Regularity Lemma
SIAM Journal on Discrete Mathematics
Erdős-Hajnal-type theorems in hypergraphs
Journal of Combinatorial Theory Series B
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The main results of this paper are regularity and counting lemmas for 3-uniform hypergraphs. A combination of these two results gives a new proof of a theorem of Frankl and Rödl, of which Szemerédi's theorem for arithmetic progressions of length 4 is a notable consequence. Frankl and Rödl also prove regularity and counting lemmas, but the proofs here, and even the statements, are significantly different. Also included in this paper is a proof of Szemerédi's regularity lemma, some basic facts about quasirandomness for graphs and hypergraphs, and detailed explanations of the motivation for the definitions used.