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


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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Correspondence to Asaf Shapira.

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Supported in part by ISF grant 224/11.

Supported in part by ISF Grant 224/11 and a Marie-Curie CIG Grant 303320.

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Moshkovitz, G., Shapira, A. A short proof of Gowers’ lower bound for the regularity lemma. Combinatorica 36, 187–194 (2016). https://doi.org/10.1007/s00493-014-3166-4

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Mathematics Subject Classification (2000)

  • 05D99