Balogh, József, Narayanan, Bhargav and Skokan, Jozef
(2019)
*The number of hypergraphs without linear cycles.*
Journal of Combinatorial Theory, Series B, 134.
pp. 309-321.
ISSN 0095-8956

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## Abstract

The r-uniform linear k-cycle C k r is the r-uniform hypergraph on k(r−1) vertices whose edges are sets of r consecutive vertices in a cyclic ordering of the vertex set chosen in such a way that every pair of consecutive edges share exactly one vertex. Here, we prove a balanced supersaturation result for linear cycles which we then use in conjunction with the method of hypergraph containers to show that for any fixed pair of integers r,k≥3, the number of C k r-free r-uniform hypergraphs on n vertices is 2 Θ(n r−1) , thereby settling a conjecture due to Mubayi and Wang from 2017.

Item Type: | Article |
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Official URL: | https://www.sciencedirect.com/journal/journal-of-c... |

Additional Information: | © 2018 Elsevier Inc |

Divisions: | Mathematics |

Subjects: | Q Science > QA Mathematics |

Sets: | Departments > Mathematics |

Date Deposited: | 02 Jul 2018 14:58 |

Last Modified: | 21 Apr 2019 23:10 |

Projects: | DMS-1500121 |

Funders: | National Science Foundation |

URI: | http://eprints.lse.ac.uk/id/eprint/88952 |

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