Tao’s Spectral Proof of the Szemerédi Regularity Lemma
نویسندگان
چکیده
On December 3, 2012, following the Third Abel conference, in honor of Endre Szemerédi, Terence Tao posted on his blog a proof of the spectral version of Szemerédi’s regularity lemma. This, in turn, proves the original version.
منابع مشابه
Remarks on Tao’s algebraic regularity lemma
We give a stability-theoretic proof of the algebraic regularity lemma from [6], in a slightly strengthened form. We also point out that the underlying lemmas hold at a greater level of generality, namely “measurable” theories and structures in the sense of Elwes-MacphersonSteinhorn.
متن کاملOn the query complexity for Showing Dense Model
A theorem of Green, Tao, and Ziegler can be stated as follows: if R is a pseudorandom distribution, and D is a dense distribution of R, then D can be modeled as a distribution M which is dense in uniform distribution such that D and M are indistinguishable. The reduction involved in the proof has exponential loss in the distinguishing probability. Reingold et al give a new proof of the theorem ...
متن کامل8 - Szemerédi ’ s Regularity Lemma
Szemerédi’s Regularity Lemma [18] tells us that every graph can be partitioned into a constant number of sets of vertices in such a way that for most of the pairs of sets in the partition, the bipartite graph of edges between them has many of the properties that one would expect in a random bipartite graph with the same expected edge density. Szemerédi originally used his lemma to prove his cel...
متن کاملA Szemerédi-type regularity lemma in abelian groups
Szemerédi’s regularity lemma is an important tool in graph theory which has applications throughout combinatorics. In this paper we prove an analogue of Szemerédi’s regularity lemma in the context of abelian groups and use it to derive some results in additive number theory. The simplest is a structure theorm for sets which are almost sum-free. If A ⊆ {1, . . . , N} has δN2 triples (a1, a2, a3)...
متن کاملThe Regularity Lemma of Szemerédi for Sparse Graphs
In this note we present a new version of the well-known lemma of Szemerédi [17] concerning regular partitions of graphs. Our result deals with subgraphs of pseudo-random graphs, and hence may be used to partition sparse graphs that do no contain dense subgraphs.
متن کامل