Let H be a fixed graph with h vertices. The graph removal lemma states that every graph on
n vertices with o (nh) copies of H can be made H-free by removing o (n 2) edges. We give a …

Sublinear Time Algorithms Page 1 Copyright © by SIAM. Unauthorized reproduction of this article
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The graph removal lemma states that any graph on n vertices with o (nh) copies of a fixed
graph H on h vertices may be made H-free by removing o (n2) edges. Despite its innocent …

Abstract The celebrated Green-Tao theorem states that there are arbitrarily long arithmetic
progressions in the primes. One of the main ingredients in their proof is a relative Szemerédi …

About twenty years ago, Green wrote a survey article on the utility of looking at toy versions
over finite fields of problems in additive combinatorics. This article was extremely influential …

Let p be a fixed prime. A triangle in is an ordered triple (x, y, z) of points satisfying x+ y+ z= 0.
Let Green proved an arithmetic triangle removal lemma which says that for every∊> 0 and …

A recently fertile strand of research in Group Theory is developing non-abelian analogues of
classical combinatorial results for arithmetic Cayley graphs, describing properties such as …

Szemerédi's regularity lemma is a fundamental tool in extremal combinatorics. However, the
original version is only helpful in studying dense graphs. In the 1990s, Kohayakawa and …

We develop a sparse graph regularity method that applies to graphs with few 4‐cycles,
including new counting and removal lemmas for 5‐cycles in such graphs. Some applications …

We prove a removal lemma for systems of linear equations over finite fields: let X 1,…, X m
be subsets of the finite field F q and let A be a (k× m) matrix with coefficients in F q; if the …