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

Text (Finding tight Hamilton cycles in random hypergraphs faster)
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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 |
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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: | 20 Jan 2021 07:11 |

URI: | http://eprints.lse.ac.uk/id/eprint/106608 |

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