A Simple Regularization of Hypergraphs

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dc.creatorIshigami, Yoshiyasu
dc.date2006-12-28
dc.date2009-04-30
dc.date.accessioned2026-07-07T13:10:03Z
dc.date.available2026-07-07T13:10:03Z
dc.descriptionWe give a simple and natural (probabilistic) construction of hypergraph regularization. It is done just by taking a constant-bounded number of random vertex samplings only one time (thus, iteration-free). It is independent from the definition of quasi-randomness and yields a new elementary proof of a strong hypergraph regularity lemma. Consequently, as an example of its applications, we have a new self-contained proof of Szemerédi's classic theorem on arithmetic progressions (1975) as well as its multidimensional extension by Furstenberg-Katznelson (1978).
dc.description16 pages
dc.identifierhttps://arxiv.org/abs/math/0612838
dc.identifierhttp://arxiv.org/abs/math/0612838
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/228938
dc.subjectCombinatorics
dc.subjectNumber Theory
dc.subject05D40, 05C65
dc.titleA Simple Regularization of Hypergraphs
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