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Results 1 - 10
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174
On characterizing hypergraph regularity
- Random Structures & Algorithms, Vol
, 2002
"... ABSTRACT: Szemerédi’s Regularity Lemma is a well-known and powerful tool in modern graph theory. This result led to a number of interesting applications, particularly in extremal graph theory. A regularity lemma for 3-uniform hypergraphs developed by Frankl and Rödl [8] allows some of the Szemeré ..."
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Cited by 2 (2 self)
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ABSTRACT: Szemerédi’s Regularity Lemma is a well-known and powerful tool in modern graph theory. This result led to a number of interesting applications, particularly in extremal graph theory. A regularity lemma for 3-uniform hypergraphs developed by Frankl and Rödl [8] allows some
An Algorithmic Hypergraph Regularity Lemma
"... Szemerédi’s Regularity Lemma is a powerful tools in graph theory. It asserts that all large graphs admit bounded partitions of their edge sets, most classes of which consist of uniformly distributed edges. The original proof of this result was non-constructive and a constructive proof was later g ..."
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given by Alon, Duke, Lefmann, Rödl and Yuster. Szemerédi’s Regularity Lemma was extended to hypergraphs by various authors. Frankl and Rödl gave one such extension in the case of 3-uniform hypergraphs, which was later extended to k-uniform hypergraphs by Rödl and Skokan. W.T. Gowers gave another
Weak hypergraph regularity and linear hypergraphs
, 2009
"... We consider conditions which allow the embedding of linear hypergraphs of fixed size. In particular, we prove that any k-uniform hypergraph H of positive uniform density contains all linear k-uniform hypergraphs of a given size. More precisely, we show that for all integers ℓ ≥ k ≥ 2 and every d&g ..."
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Cited by 20 (6 self)
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in the proof of this result is a counting lemma for linear hypergraphs, which establishes that the straightforward extension of graph ε-regularity to hypergraphs suffices for counting linear hypergraphs. We also consider some related problems.
Regular partitions of hypergraphs: Regularity Lemmas
- COMBIN. PROBAB. COMPUT
, 2007
"... Szemerédi’s regularity lemma for graphs has proved to be a powerful tool with many subsequent applications. The objective of this paper is to extend the techniques developed by Nagle, Skokan, and authors and obtain a stronger and more “user friendly” regularity lemma for hypergraphs. ..."
Abstract
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Cited by 29 (1 self)
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Szemerédi’s regularity lemma for graphs has proved to be a powerful tool with many subsequent applications. The objective of this paper is to extend the techniques developed by Nagle, Skokan, and authors and obtain a stronger and more “user friendly” regularity lemma for hypergraphs.
An algorithmic version of the hypergraph regularity method
- PROCEEDINGS OF THE IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE
, 2005
"... Extending the Szemerédi Regularity Lemma for graphs, P. Frankl and V. Rödl [14] established a 3-graph Regularity Lemma guaranteeing that all large triple systems Gn admit bounded partitions of their edge sets, most classes of which consist of regularly distributed triples. Many applications of t ..."
Abstract
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Cited by 11 (7 self)
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Extending the Szemerédi Regularity Lemma for graphs, P. Frankl and V. Rödl [14] established a 3-graph Regularity Lemma guaranteeing that all large triple systems Gn admit bounded partitions of their edge sets, most classes of which consist of regularly distributed triples. Many applications
A hypergraph regularity method for generalized Turán problems
- Random Structures & Algorithms
"... ABSTRACT: We describe a method that we believe may be foundational for a comprehensive theory of generalized Turán problems. The cornerstone of our approach is a quasirandom counting lemma for quasirandom hypergraphs, which extends the standard counting lemma by not only counting copies of a particu ..."
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Cited by 8 (0 self)
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ABSTRACT: We describe a method that we believe may be foundational for a comprehensive theory of generalized Turán problems. The cornerstone of our approach is a quasirandom counting lemma for quasirandom hypergraphs, which extends the standard counting lemma by not only counting copies of a
A hypergraph regularity method for generalised Turán problems
, 2008
"... We describe a method that we believe may be foundational for a comprehensive theory of generalised Turán problems. The cornerstone of our approach is a quasirandom counting lemma for quasirandom hypergraphs, which extends the standard counting lemma by not only counting copies of a particular config ..."
Abstract
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Cited by 2 (1 self)
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We describe a method that we believe may be foundational for a comprehensive theory of generalised Turán problems. The cornerstone of our approach is a quasirandom counting lemma for quasirandom hypergraphs, which extends the standard counting lemma by not only counting copies of a particular
A simple regularization of hypergraphs
, 2009
"... We give a simple and natural construction of hypergraph regularization. It yields a short proof of a hypergraph regularity lemma. Consequently, as an example of its applications, we have a short self-contained proof of Szemerédi’s classic theorem on arithmetic progressions (1975) as well as its mult ..."
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Cited by 6 (3 self)
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We give a simple and natural construction of hypergraph regularization. It yields a short proof of a hypergraph regularity lemma. Consequently, as an example of its applications, we have a short self-contained proof of Szemerédi’s classic theorem on arithmetic progressions (1975) as well as its
Results 1 - 10
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174
