Lectures on Discrete Geometry
Extremal problems on set systems
Random Structures & Algorithms
The regularity lemma and its applications in graph theory
Theoretical aspects of computer science
The Regularity Lemma and Its Applications in Graph Theory
Theoretical Aspects of Computer Science, Advanced Lectures [First Summer School on Theoretical Aspects of Computer Science, Tehran, Iran, July 2000]
Regularity properties for triple systems
Random Structures & Algorithms
A Note on a Question of Erdös and Graham
Combinatorics, Probability and Computing
Regularity lemma for k-uniform hypergraphs
Random Structures & Algorithms
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
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
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
Exact minimum degree thresholds for perfect matchings in uniform hypergraphs
Journal of Combinatorial Theory Series A
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
A hypergraph Turán theorem via lagrangians of intersecting families
Journal of Combinatorial Theory Series A
Counting substructures II: Hypergraphs
Combinatorica
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In this article we discuss several combinatorial problems that can be addressed by the Regularity Method for hypergraphs. Based on the recent results of Nagle, Schacht, and the authors, we give here solutions to these problems.In particular, we prove the following: Let ℱ be a k-uniform hypergraph on t vertices and suppose an n-vertex k-uniform hypergraph ℋ contains only o(nt) copies of ℱ. Then one can delete o(nk) edges of ℋ to make it ℱ-free.Similar results were recently obtained by W. T. Gowers. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006