Allen, Peter, Koch, Christoph, Parczyk, Olaf and Person, Yury
(2018)
*Finding tight hamilton cycles in random hypergraphs faster.*
In: Bender, M., Farach-Colton, M. and Mosteiro, M., (eds.)
LATIN 2018: theoretical informatics.
Lecture Notes in Computer Science (10807).
Springer, Cham, Switzerland, pp. 28-36.
ISBN 9783319774039

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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 Clog3n/n . Our result partially answers a question of Dudek and Frieze (Random Struct Algorithms 42:374–385, 2013) who proved that tight Hamilton cycles exists 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 et al. (Random Struct Algorithms 46:446–465, 2015) and Nenadov and Škorić (arXiv:1601.04034) 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≥Clog8n/n .

Item Type: | Book Section |
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Official URL: | https://link.springer.com/book/10.1007/978-3-319-7... |

Additional Information: | © 2018 Springer International Publishing AG, part of Springer Nature |

Divisions: | Mathematics |

Subjects: | Q Science > QA Mathematics |

Date Deposited: | 18 May 2018 10:24 |

Last Modified: | 20 Aug 2021 01:15 |

Projects: | P26826, 639046, PE 2299/1-1 |

Funders: | Austrian Science Fund, European Research Council, DFG grant |

URI: | http://eprints.lse.ac.uk/id/eprint/88000 |

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