Letzter, Shoham;
(2023)
Hypergraphs with no tight cycles.
Proceedings of the American Mathematical Society
10.1090/proc/16043.
(In press).
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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-pp.ucl.ac.uk/id/eprint/10148692 |
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