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
The regularity lemma and its applications in graph theory
Theoretical aspects of computer science
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
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
Counting Small Cliques in 3-uniform Hypergraphs
Combinatorics, Probability and Computing
Counting subgraphs in quasi-random 4-uniform hypergraphs
Random Structures & Algorithms - Proceedings of the Eleventh International Conference "Random Structures and Algorithms," August 9—13, 2003, Poznan, Poland
An Algorithmic Version of the Hypergraph Regularity Method
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
A Dirac-Type Theorem for 3-Uniform Hypergraphs
Combinatorics, Probability and Computing
Quasirandomness, Counting and Regularity for 3-Uniform Hypergraphs
Combinatorics, Probability and Computing
Applications of the regularity lemma for uniform hypergraphs
Random Structures & Algorithms
Arithmetic Progressions in Sets with Small Sumsets
Combinatorics, Probability and Computing
The Ramsey number for hypergraph cycles I
Journal of Combinatorial Theory Series A
An Algorithmic Version of the Hypergraph Regularity Method
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Quasirandomness, Counting and Regularity for 3-Uniform Hypergraphs
Combinatorics, Probability and Computing
Applications of the regularity lemma for uniform hypergraphs
Random Structures & Algorithms
Arithmetic Progressions in Sets with Small Sumsets
Combinatorics, Probability and Computing
A variant of the hypergraph removal lemma
Journal of Combinatorial Theory Series A
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
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
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
Hypergraph regularity and quasi-randomness
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
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
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
On the removal lemma for linear systems over Abelian groups
European Journal of Combinatorics
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
Counting substructures II: Hypergraphs
Combinatorica
Hi-index | 0.00 |
Szemerédi's Regularity Lemma proved to be a powerful tool in the area of extremal graph theory. Many of its applications are based on its accompanying Counting Lemma: If G is an ℓ-partite graph with V (G) = V1 ∪ … ∪ Vℓ and ∣Vi∣ = n for all i ∈ [ℓ], and all pairs (Vi, Vj) are ε-regular of density d for 1 ≤ i ≤ j ≤ ℓ and ε ≪ d, then G contains $(1\pm f_{\ell}(\varepsilon))d^{\ell \choose 2}\times n^{\ell}$ cliques Kℓ, where fℓ(ε) → 0 as ε → 0.Recently, Rödl and Skokan generalized Szemerédi's Regularity Lemma from graphs to k-uniform hypergraphs for arbitrary k ≥ 2. In this paper we prove a Counting Lemma accompanying the Rödl–Skokan hypergraph Regularity Lemma. Similar results were independently obtained by Gowers.Such results give combinatorial proofs to the density result of Szemerédi and some of the density theorems of Furstenberg and Katznelson. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2006