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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
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).
D. Conlon and J. Fox: Bounds for graph regularity and removal lemmas, GAFA 22 (2012), 1191–1256.
T. Gowers: Lower bounds of tower type for Szemerédi’s uniformity lemma, GAFA 7 (1997), 322–337.
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.
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported in part by ISF grant 224/11.
Supported in part by ISF Grant 224/11 and a Marie-Curie CIG Grant 303320.
Rights and permissions
About this article
Cite this article
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
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00493-014-3166-4