Hypergraphs with no tight cycles

Abstract

We show that every $r$-uniform hypergraph on $n$ vertices which does not contain a tight cycle 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 up 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.

arXiv comment9 pages; corrected typos