Hypergraphs, quasi-randomness, and conditions for regularity
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
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
Hereditary properties of hypergraphs
Journal of Combinatorial Theory Series B
Note: A combinatorial proof of the Removal Lemma for Groups
Journal of Combinatorial Theory Series A
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
The 3-colour ramsey number of a 3-uniform berge cycle
Combinatorics, Probability and Computing
Approximate Hypergraph Partitioning and Applications
SIAM Journal on Computing
Green's conjecture and testing linear invariant properties
Property testing
Green's conjecture and testing linear invariant properties
Property testing
Testable and untestable classes of first-order formulae
Journal of Computer and System Sciences
SIAM Journal on Discrete Mathematics
Counting substructures II: Hypergraphs
Combinatorica
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Recent work of Gowers [T. Gowers, A new proof of Szemerédi's theorem, Geom. Funct. Anal. 11 (2001) 465-588] and Nagle, Rödl, Schacht, and Skokan [B. Nagle, V. Rödl, M. Schacht, The counting lemma for regular k-uniform hypergraphs, Random Structures Algorithms, in press; V. Rödl, J. Skokan, Regularity lemma for k-uniform hypergraphs, Random Structures Algorithms, in press; V. Rödl, J. Skokan, Applications of the regularity lemma for uniform hypergraphs, preprint] has established a hypergraph removal lemma, which in turn implies some results of Szemerédi [E. Szemerédi, On sets of integers containing no k elements in arithmetic progression, Acta Arith. 27 (1975) 299-345], and Furstenberg and Katznelson [H. Furstenberg, Y. Katznelson, An ergodic Szemerédi theorem for commuting transformations, J. Anal. Math. 34 (1978) 275-291] concerning one-dimensional and multidimensional arithmetic progressions, respectively. In this paper we shall give a self-contained proof of this hypergraph removal lemma. In fact we prove a slight strengthening of the result, which we will use in a subsequent paper [T. Tao, The Gaussian primes contain arbitrarily shaped constellations, preprint] to establish (among other things) infinitely many constellations of a prescribed shape in the Gaussian primes.