Finding tight Hamilton cycles in random hypergraphs faster

Allen, Peter ORCID: 0000-0001-6555-3501, 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:	04 Oct 2024 20:39
URI:	http://eprints.lse.ac.uk/id/eprint/106608

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