8 - Szemerédi ’ s Regularity Lemma
نویسنده
چکیده
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 celebrated theorem that sets of integers of positive density contain arbitrarily long arithmetic progressions [19]. Since the first version of the regularity lemma, the lemma has been extended a generalized and applied in many different areas of mathematics, in particular, in Green and Tao’s proof [13] that the primes contain arbitrarily long arithmetic progressions. The lemma has also been generalized by a number of authors (see Gowers [11]) to hypergraphs.
منابع مشابه
Tao’s Spectral Proof of the Szemerédi Regularity Lemma
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.
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