The Uniformity Lemma for hypergraphs

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 1992 English Publisher:Springer Science and Business Media LLCJournal:Graphs and Combinatorics, volume 8, pages 309-312 (issn: 0911-0119, eissn: 1435-5914,

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Authors: Peter Frankl; Vojtech Rödl;

doi: 10.1007/bf02351586

The Uniformity Lemma for hypergraphs

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Abstract

This is an extension of Szemerédi's theorem called the Uniformity Lemma for Graphs (see \textit{E. Szemerédi} [Problèmes combinatoires et théorie des graphes, Orsay 1976, Colloq. int. CNRS No. 260, 399-401 (1978; Zbl 0413.05055)]) to \(r\)-uniform hypergraphs. Two applications of the result are announced: proof of a conjecture of Erdős concerning Turán-type problem, and giving an alternative condition for quasirandomness.

Related Organizations

Centre national de la recherche scientifique
France
Emory University
United States
French National Centre for Scientific Research
France

Keywords

Extremal problems in graph theory, hypergraphs, uniformity lemma, Hypergraphs, Szemerédi's theorem

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