A short proof of Gowers’ lower bound for the regularity lemma

Guy Moshkovitz; Asaf Shapira

doi:10.1007/s00493-014-3166-4

A short proof of Gowers’ lower bound for the regularity lemma

Guy Moshkovitz, Asaf Shapira

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

A celebrated result of Gowers states that for every є>0 there is a graph G such that every є-regular partition of G (in the sense of Szemerédi’s regularity lemma) has order given by a tower of exponents of height polynomial in 1/є. In this note we give a new proof of this result that uses a construction and proof of correctness that are significantly simpler and shorter.

Original language	English
Pages (from-to)	187-194
Number of pages	8
Journal	Combinatorica
Volume	36
Issue number	2
DOIs	https://doi.org/10.1007/s00493-014-3166-4
State	Published - 1 Apr 2016

Keywords

05D99

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics
Computational Mathematics

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10.1007/s00493-014-3166-4

Cite this

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abstract = "A celebrated result of Gowers states that for every є>0 there is a graph G such that every є-regular partition of G (in the sense of Szemer{\'e}di{\textquoteright}s regularity lemma) has order given by a tower of exponents of height polynomial in 1/є. In this note we give a new proof of this result that uses a construction and proof of correctness that are significantly simpler and shorter.",

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N2 - A celebrated result of Gowers states that for every є>0 there is a graph G such that every є-regular partition of G (in the sense of Szemerédi’s regularity lemma) has order given by a tower of exponents of height polynomial in 1/є. In this note we give a new proof of this result that uses a construction and proof of correctness that are significantly simpler and shorter.

AB - A celebrated result of Gowers states that for every є>0 there is a graph G such that every є-regular partition of G (in the sense of Szemerédi’s regularity lemma) has order given by a tower of exponents of height polynomial in 1/є. In this note we give a new proof of this result that uses a construction and proof of correctness that are significantly simpler and shorter.

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A short proof of Gowers’ lower bound for the regularity lemma

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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