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

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.

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References

  1. [1]

    B. Bollobás: The work of William Timothy Gowers, Proc. of the ICM, Vol. I (Berlin, 1998). Doc. Math., Extra Vol. I, 1998, 109–118 (electronic).

    Google Scholar 

  2. [2]

    D. Conlon and J. Fox: Bounds for graph regularity and removal lemmas, GAFA 22 (2012), 1191–1256.

    MathSciNet  MATH  Google Scholar 

  3. [3]

    T. Gowers: Lower bounds of tower type for Szemerédi’s uniformity lemma, GAFA 7 (1997), 322–337.

    MathSciNet  MATH  Google Scholar 

  4. [4]

    J. Komlós and M. Simonovits: Szemerédi’s Regularity Lemma and its applications in graph theory, in: Combinatorics, Paul Erdős is Eighty, Vol II (D. Miklós, V. T. Sós, T. Szönyi eds.), János Bolyai Math. Soc., Budapest (1996), 295–352.

    MATH  Google Scholar 

  5. [5]

    E. Szemerédi: Regular partitions of graphs, in: Proc. Colloque Inter. CNRS (J. C. Bermond, J. C. Fournier, M. Las Vergnas and D. Sotteau, eds.), 1978, 399–401.

    Google Scholar 

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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