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416
A variant of the hypergraph removal lemma
, 2006
"... Abstract. Recent work of Gowers [10] and Nagle, Rödl, Schacht, and Skokan [15], [19], [20] has established a hypergraph removal lemma, which in turn implies some results of Szemerédi [26] and Furstenberg-Katznelson [7] concerning one-dimensional and multi-dimensional arithmetic progressions respecti ..."
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Cited by 75 (7 self)
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Abstract. Recent work of Gowers [10] and Nagle, Rödl, Schacht, and Skokan [15], [19], [20] has established a hypergraph removal lemma, which in turn implies some results of Szemerédi [26] and Furstenberg-Katznelson [7] concerning one-dimensional and multi-dimensional arithmetic progressions
A correspondence principle between (hyper)graph theory and probability theory, and the (hyper)graph removal lemma
, 2006
"... We introduce a correspondence principle (analogous to the Furstenberg correspondence principle) that allows one to extract an infinite random graph or hypergraph from a sequence of increasingly large deterministic graphs or hypergraphs. As an application we present a new (infinitary) proof of the hy ..."
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Cited by 34 (8 self)
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of the hypergraph removal lemma of Nagle-Schacht-Rödl-Skokan and Gowers, which does not require the hypergraph regularity lemma and requires significantly less computation. This in turn gives new proofs of several corollaries of the hypergraph removal lemma, such as Szemerédi’s theorem on arithmetic progressions.
THE SYMMETRY PRESERVING REMOVAL LEMMA
, 2009
"... In this paper we observe that in the hypergraph removal lemma, the edge removal can be done in such a way that the symmetries of the original hypergraph remain preserved. As an application we prove the following generalization of Szemerédi’s Theorem on arithmetic progressions. Let A be an Abelian g ..."
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Cited by 4 (0 self)
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In this paper we observe that in the hypergraph removal lemma, the edge removal can be done in such a way that the symmetries of the original hypergraph remain preserved. As an application we prove the following generalization of Szemerédi’s Theorem on arithmetic progressions. Let A be an Abelian
Property testing in hypergraphs and the removal lemma (Extended Abstract)
, 2006
"... Property testers are efficient, randomized algorithms which recognize if an input graph (or other combinatorial structure) satisfies a given property or if it is “far” from exhibiting it. Generalizing several earlier results, Alon and Shapira showed that hereditary graph properties are testable (wit ..."
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Cited by 11 (0 self)
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(with one-sided error). In this paper we prove the analogous result for hypergraphs. This result is an immediate consequence of a (hyper)graph theoretic statement, which is an extension of the so-called removal lemma. The proof of this generalization relies on the regularity method for hypergraphs.
A Removal Lemma for Systems of Linear Equations over Finite Fields
, 2008
"... We prove a removal lemma for systems of linear equations over finite fields: let X1,..., Xm be subsets of the finite field Fq and let A be a (k×m) matrix with coefficients in Fq and rank k; if the linear system Ax = b has o(q m−k) solutions with xi ∈ Xi, then we can destroy all these solutions by de ..."
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Cited by 29 (2 self)
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conjectured by Green. Our proof uses the colored version of the hypergraph Removal Lemma.
Generalizations of the removal lemma
, 2006
"... Ruzsa and Szemerédi established the triangle removal lemma by proving that: For every η> 0 there exists c> 0 so that every sufficiently large graph on n vertices, which contains at most cn3 triangles can be made triangle free by removal of at most η `n ´ edges. More general statements of that ..."
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Cited by 9 (1 self)
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Ruzsa and Szemerédi established the triangle removal lemma by proving that: For every η> 0 there exists c> 0 so that every sufficiently large graph on n vertices, which contains at most cn3 triangles can be made triangle free by removal of at most η `n ´ edges. More general statements
Removal lemma for infinitely-many forbidden hypergraphs and property testing
, 2008
"... We prove a removal lemma for infinitely-many forbidden hypergraphs. It affirmatively settles a question on property testing raised by Alon and Shapira (2005) [2, 3]. All monotone hypergraph properties and all hereditary partite hypergraph properties are testable. Our proof constructs a constant-tim ..."
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Cited by 6 (5 self)
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We prove a removal lemma for infinitely-many forbidden hypergraphs. It affirmatively settles a question on property testing raised by Alon and Shapira (2005) [2, 3]. All monotone hypergraph properties and all hereditary partite hypergraph properties are testable. Our proof constructs a constant
Removal Lemma for null sets
, 2013
"... The Removal Lemma (more generally, the Alon–Shapira Theorem 15.24) has a graphon analogue, where instead of talking about sets of small measure, we talk about nullsets. Besides the version stated and proved below, such analogues were given by Svante Janson ([3], Lemma 5.3) and more recently by Fedor ..."
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The Removal Lemma (more generally, the Alon–Shapira Theorem 15.24) has a graphon analogue, where instead of talking about sets of small measure, we talk about nullsets. Besides the version stated and proved below, such analogues were given by Svante Janson ([3], Lemma 5.3) and more recently
The counting lemma for regular k-uniform hypergraphs
, 2004
"... 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 ..."
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Cited by 105 (14 self)
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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
An Algorithmic Regularity Lemma For Hypergraphs
- SIAM J. COMPUT
, 2000
"... In this paper, we will consider the problem of designing an efficient algorithm that finds an -regular partition of an l-uniform hypergraph. ..."
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Cited by 19 (5 self)
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In this paper, we will consider the problem of designing an efficient algorithm that finds an -regular partition of an l-uniform hypergraph.
Results 1 - 10
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416
