Tight Hamilton cycles in random hypergraphs

Allen, Peter ORCID: 0000-0001-6555-3501, Böttcher, Julia ORCID: 0000-0002-4104-3635, Kohayakawa, Yoshiharu and Person, Yury (2015) Tight Hamilton cycles in random hypergraphs. Random Structures and Algorithms, 46 (3). pp. 446-465. ISSN 1042-9832

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Abstract

We give an algorithmic proof for the existence of tight Hamilton cycles in a random r-uniform hypergraph with edge probability p=n-1+ε for every ε>0. This partly answers a question of Dudek and Frieze (Random Struct Algor 42 (2013), 374-385), who used a second moment method to show that tight Hamilton cycles exist even for p=ω(n)/n(r≥3) where ω(n)→∞ arbitrary slowly, and for p=(e+o(1))/n(r≥4). The method we develop for proving our result applies to related problems as well.

Item Type:	Article
Official URL:	http://onlinelibrary.wiley.com/journal/10.1002/(IS...
Additional Information:	© 2015 Wiley
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	12 Dec 2013 14:27
Last Modified:	01 Oct 2024 03:41
URI:	http://eprints.lse.ac.uk/id/eprint/54873

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