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Hypergraph regularity method is a powerful tool that refers to the combined application of hypergraph regularity lemma and associated counting lemma. It is a generalization of graph regularity method, which refers to the use of [[Szemerédi regularity lemma|Szemerédi's regularity]] and counting lemmas.
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There are several distinct formulations of the method, all of which imply [[hypergraph removal lemma]] and a number of other powerful results, such as [[Szemerédi's theorem]], as well as some of its multidimensional extensions. The following formulations are due to [[Vojtěch Rödl|V. Rödl]], B. Nagle, J. Skokan, [[Mathias Schacht|M. Schacht]], and [[Yoshiharu Kohayakawa|Y. Kohayakawa]]<ref>{{Cite journal|last=Rödl|first=V.|last2=Nagle|first2=B.|last3=Skokan|first3=J.|last4=Schacht|first4=M.|last5=Kohayakawa|first5=Y.|date=2005-06-07|title=The hypergraph regularity method and its applications|url=https://www.pnas.org/content/102/23/8109|journal=Proceedings of the National Academy of Sciences|language=en|volume=102|issue=23|pages=8109–8113|doi=10.1073/pnas.0502771102|issn=0027-8424|pmc=PMC1149431|pmid=15919821}}</ref>, for alternative versions see [[Terence Tao|Tao]] (2006)<ref>{{Cite journal|last=Tao|first=Terence|date=2006-10-01|title=A variant of the hypergraph removal lemma|url=https://www.sciencedirect.com/science/article/pii/S0097316505002177|journal=Journal of Combinatorial Theory, Series A|language=en|volume=113|issue=7|pages=1257–1280|doi=10.1016/j.jcta.2005.11.006|issn=0097-3165}}</ref>, and [[Timothy Gowers|Gowers]] (2007)<ref>{{Cite journal|last=Gowers|first=William|date=2007-11-01|title=Hypergraph regularity and the multidimensional Szemerédi theorem|url=http://doi.org/10.4007/annals.2007.166.897|journal=Annals of Mathematics|volume=166|issue=3|pages=897–946|doi=10.4007/annals.2007.166.897|issn=0003-486X}}</ref>.
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== Definitions ==
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