A tight lower bound for Szemerédi’s regularity lemma

Abstract

We determine the order of the tower height for the partition size in a version of Szemerédi’s regularity lemma. This addresses a question of Gowers.

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Correspondence to László Miklós Lovász.

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Research supported by a Packard Fellowship, by a Simons Fellowship, by NSF grant DMS-1069197, by an Alfred P. Sloan Fellowship, and by an MIT NEC Corporation Award.

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Fox, J., Lovász, L.M. A tight lower bound for Szemerédi’s regularity lemma. Combinatorica 37, 911–951 (2017). https://doi.org/10.1007/s00493-016-3274-4

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Mathematics Subject Classification (2000)

  • 05C75