Quasirandomness in hypergraphs

Elad Aigner-Horev, David Conlon, Hiệp Hàn, Yury Person, Mathias Schacht

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

An n-vertex graph G of edge density p is considered to be quasirandom if it shares several important properties with the random graph G(n, p). A well-known theorem of Chung, Graham and Wilson states that many such ‘typical’ properties are asymptotically equivalent and, thus, a graph G possessing one such property automatically satisfies the others. In recent years, work in this area has focused on uncovering more quasirandom graph properties and on extending the known results to other discrete structures. In the context of hypergraphs, however, one may consider several different notions of quasirandomness. A complete description of these notions has been provided recently by Towsner, who proved several central equivalences using an analytic framework. We give short and purely combinatorial proofs of the main equivalences in Towsner’s result.

Original languageEnglish
Article number#P3.34
JournalElectronic Journal of Combinatorics
Volume25
Issue number3
DOIs
StatePublished - 24 Aug 2018

Keywords

  • Hypergraphs
  • Quasirandom

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