The poset of hypergraph quasirandomness1. Issue 4 (25th November 2013)

• Record Type: Journal Article
• Authors: Lenz, John; Mubayi, Dhruv
• Is Part Of: Random structures & algorithms. Volume 46:Issue 4(2015)
• Page Start: 762
• Page End: 800
• Publication Date: 2013-11-25
• Subjects: Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20521
• Languages: English
• ISSNs: 1042-9832

Abstract

<abstract abstract-type="main"> <title>Abstract</title> <p>Chung and Graham began the systematic study of <italic>k</italic>‐uniform hypergraph quasirandom properties soon after the foundational results of Thomason and Chung‐Graham‐Wilson on quasirandom graphs. One feature that became apparent in the early work on <italic>k</italic>‐uniform hypergraph quasirandomness is that properties that are equivalent for graphs are not equivalent for hypergraphs, and thus hypergraphs enjoy a variety of inequivalent quasirandom properties. In the past two decades, there has been an intensive study of these disparate notions of quasirandomness for hypergraphs, and an open problem that has emerged is to determine the relationship between them.</p> <p>Our main result is to determine the poset of implications between these quasirandom properties. This answers a recent question of Chung and continues a project begun by Chung and Graham in their first paper on hypergraph quasirandomness in the early 1990's. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46, 762–800, 2015</p> </abstract>