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)
- Accepted Version
Repository staff only until 23 March 2021. Download (426kB) | Request a copy |

## 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 log3 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 randomised polynomial time algorithm working for edge probabilities p ≥ n−1+ε , while the algorithm of Nenadov and Škorić is a randomised quasipolynomial time algorithm working for edge probabilities p ≥ C log8 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: | 14 Oct 2020 09:08 |

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

### Actions (login required)

View Item |