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Graph removal lemmas
 SURVEYS IN COMBINATORICS
, 2013
"... The graph removal lemma states that any graph on n vertices with o(nv(H)) copies of a fixed graph H may be made Hfree by removing o(n²) edges. Despite its innocent appearance, this lemma and its extensions have several important consequences in number theory, discrete geometry, graph theory and com ..."
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Cited by 9 (3 self)
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The graph removal lemma states that any graph on n vertices with o(nv(H)) copies of a fixed graph H may be made Hfree by removing o(n²) edges. Despite its innocent appearance, this lemma and its extensions have several important consequences in number theory, discrete geometry, graph theory
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 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
Deducing the density HalesJewett theorem from an infinitary removal lemma
 J. Theoret. Probab
"... 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
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 FurstenbergKatznelson [7] concerning onedimensional and multidimensional 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 FurstenbergKatznelson [7] concerning onedimensional and multidimensional arithmetic progressions
A combinatorial proof of the Removal Lemma for Groups
"... Green [Geometric and Functional Analysis 15 (2005), 340–376] established a version of the Szemerédi Regularity Lemma for abelian groups and derived the Removal Lemma for abelian groups as its corollary. We provide another proof of his Removal Lemma that allows us to extend its statement to all finit ..."
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Cited by 29 (3 self)
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Green [Geometric and Functional Analysis 15 (2005), 340–376] established a version of the Szemerédi Regularity Lemma for abelian groups and derived the Removal Lemma for abelian groups as its corollary. We provide another proof of his Removal Lemma that allows us to extend its statement to all
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