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The number of hypergraphs without linear cycles

Balogh, József, Narayanan, Bhargav and Skokan, Jozef ORCID: 0000-0003-3996-7676 (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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Identification Number: 10.1016/j.jctb.2018.07.003

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
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: 20 Sep 2021 03:08
Projects: DMS-1500121
Funders: National Science Foundation
URI: http://eprints.lse.ac.uk/id/eprint/88952

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