Hamilton cycles in quasirandom hypergraphs1. Issue 2 (26th February 2016)

• Record Type: Journal Article
• Authors: Lenz, John; Mubayi, Dhruv; Mycroft, Richard
• Is Part Of: Random structures & algorithms. Volume 49:Issue 2(2016)
• Page Start: 363
• Page End: 378
• Publication Date: 2016-02-26
• Subjects: hypergraphs -- Hamilton cycles -- quasirandomness; Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20638
• Languages: English
• ISSNs: 1042-9832

Abstract

Abstract: We show that, for a natural notion of quasirandomness in k ‐uniform hypergraphs, any quasirandom k ‐uniform hypergraph on n vertices with constant edge density and minimum vertex degree Ω( n k ‐1 ) contains a loose Hamilton cycle. We also give a construction to show that a k ‐uniform hypergraph satisfying these conditions need not contain a Hamilton ℓ ‐cycle if k – ℓ divides k . The remaining values of ℓ form an interesting open question. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 363–378, 2016