Finding tight Hamilton cycles in random hypergraphs faster

Allen, Peter, Koch, Christoph, Parczyk, Olaf and Person, Yury (2020) Finding tight Hamilton cycles in random hypergraphs faster. Combinatorics, Probability and Computing. ISSN 0963-5483

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Abstract

In an r-uniform hypergraph on n vertices, a tight Hamilton cycle consists of n edges such that there exists a cyclic ordering of the vertices where the edges correspond to consecutive segments of r vertices. We provide a first deterministic polynomial-time algorithm, which finds a.a.s. tight Hamilton cycles in random r-uniform hypergraphs with edge probability at least C log 3 n/n. Our result partially answers a question of Dudek and Frieze, who proved that tight Hamilton cycles exist already for p = ω(1/n) for r = 3 and p = (e + o(1))/n for r ≽ 4 using a second moment argument. Moreover our algorithm is superior to previous results of Allen, Böttcher, Kohayakawa and Person, and Nenadov and Škorić, in various ways: the algorithm of Allen et al. is a randomized polynomial-time algorithm working for edge probabilities p ≽ n −1+ ε, while the algorithm of Nenadov and Škorić is a randomized quasipolynomial-time algorithm working for edge probabilities p ≽ C log 8 n/n.

Item Type:	Article
Official URL:	https://www.cambridge.org/core/journals/combinator...
Additional Information:	© 2020 The Authors
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Date Deposited:	23 Sep 2020 09:33
Last Modified:	08 May 2024 20:29
URI:	http://eprints.lse.ac.uk/id/eprint/106608

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