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The number of hypergraphs without linear cycles

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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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: 15 Aug 2019 23:07
Projects: DMS-1500121
Funders: National Science Foundation
URI: http://eprints.lse.ac.uk/id/eprint/88952

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