Extremal problems on set systems
Random Structures & Algorithms
Integer and fractional packings in dense 3-uniform hypergraphs
Random Structures & Algorithms
Hereditary Properties of Triple Systems
Combinatorics, Probability and Computing
Counting Small Cliques in 3-uniform Hypergraphs
Combinatorics, Probability and Computing
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
Hereditary Properties of Triple Systems
Combinatorics, Probability and Computing
Regularity lemma for k-uniform hypergraphs
Random Structures & Algorithms
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
A Dirac-Type Theorem 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 co-degree density of the Fano plane
Journal of Combinatorial Theory Series B
Loose Hamilton cycles in 3-uniform hypergraphs of high minimum degree
Journal of Combinatorial Theory Series B
3-Uniform hypergraphs of bounded degree have linear Ramsey numbers
Journal of Combinatorial Theory Series B
Combinatorial Problems for Horn Clauses
Graph Theory, Computational Intelligence and Thought
Complete Partite subgraphs in dense hypergraphs
Random Structures & Algorithms
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Szemerédi's Regularity Lemma proved to be a powerful tool in the area of extremal graph theory [J. Komlós and M. Simonovits, Szemerédi's Regularity Lemma and its applications in graph theory, Combinatorics 2 (1996), 295-352]. Many of its applications are based on the following technical fact: If G is a k-partite graph with V(G) = ∪ki=1 Vi, |Vi| = n for all i ∈ [k], and all pairs {Vi, Vj}, 1 ≤ i j ≤ k, are ε-regular of density d, then G contains d??nk(1 + f(ε)) cliques K(2)k, where f(ε) → 0 as ε → 0. The aim of this paper is to establish the analogous statement for 3-uniform hypergraphs. Our result, to which we refer as The Counting Lemma, together with Theorem 3.5 of P. Frankl and V. Rödl [Extremal problems on set systems, Random Structures Algorithms 20(2) (2002), 131-164), a Regularity Lemma for Hypergraphs, can be applied in various situations as Szemerédi's Regularity Lemma is for graphs. Some of these applications are discussed in previous papers, as well as in upcoming papers, of the authors and others.