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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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
Date Deposited:	02 Jul 2018 14:58
Last Modified:	16 Apr 2024 03:27
Projects:	DMS-1500121
Funders:	National Science Foundation
URI:	http://eprints.lse.ac.uk/id/eprint/88952

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