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Hypergraphs with no tight cycles

Letzter, Shoham; (2023) Hypergraphs with no tight cycles. Proceedings of the American Mathematical Society 10.1090/proc/16043. (In press). Green open access

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Abstract

We show that every r-uniform hypergraph on n vertices which does not contain a tight cycle has has at most O(n^{r-1}(log n)^{5}) edges. This is an improvement on the previously best-known bound, of n^{r-1}e^{O(\sqrt{log n})} due to Sudakov and Tomon, and our proof builds on their work. A recent construction of B. Janzer implies that our bound is tight up to an O((log n)^{4} log log n) factor.

Type: Article
Title: Hypergraphs with no tight cycles
Open access status: An open access version is available from UCL Discovery
DOI: 10.1090/proc/16043
Publisher version: https://www.ams.org/journals/proc/earlyview/
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions.
UCL classification: UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL
URI: https://discovery.ucl.ac.uk/id/eprint/10148692
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