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Szemerédi's regularity lemma revisited

Terence Tao
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Abstract

Szemerédi's regularity lemma is a basic tool in graph theory, and also plays an important role in additive combinatorics, most notably in proving Szemerédi's theorem on arithmetic progressions . In this note we revisit this lemma from the perspective of probability theory and information theory instead of graph theory, and observe a variant of this lemma which introduces a new parameter $F$. This stronger version of the regularity lemma was iterated in a recent paper of the author to reprove the analogous regularity lemma for hypergraphs.

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Terence Tao. 2005-11-16. Szemerédi's regularity lemma revisited. https://arxiv.org/abs/math/0504472

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