Hypergraphs, Quasi-randomness, and Conditions for Regularity
نویسندگان
چکیده
منابع مشابه
Hypergraphs, Quasi-randomness, and Conditions for Regularity
Haviland and Thomason and Chung and Graham were the first to investigate systematically some properties of quasi-random hypergraphs. In particular, in a series of articles, Chung and Graham considered several quite disparate properties of random-like hypergraphs of density 1/2 and proved that they are in fact equivalent. The central concept in their work turned out to be the so called deviation...
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Thomason and Chung, Graham, and Wilson were the first to systematically study quasi-random graphs and hypergraphs, and proved that several properties of random graphs imply each other in a deterministic sense. Their concepts of quasi-randomness match the notion of ε-regularity from the earlier Szemerédi regularity lemma. In contrast, there exists no “natural” hypergraph regularity lemma matchin...
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The first half of this paper is mainly expository, and aims at introducing the regularity lemma of Szemerédi. Among others, we discuss an early application of the regularity lemma that relates the notions of universality and uniform distribution of edges, a form of ‘pseudorandomness’ or ‘quasi-randomness’. We then state two closely related variants of the regularity lemma for sparse graphs and ...
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Quasi-random properties are deterministic properties which capture certain characteristics of random objects. The last decades have seen an extensive e↵ort in the study of this subject which has revealed many connections between di↵erent branches of mathematics and theoretical computer science. For graphs the systematic investigation was initiated by Thomason [27, 28] who studied deterministic ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2002
ISSN: 0097-3165
DOI: 10.1006/jcta.2001.3217