On hypergraphs without loose cycles

Abstract

Recently, Mubayi and Wang showed that for $r\ge 4$ and $\ell \ge 3$, the number of $n$-vertex $r$-graphs that do not contain any loose cycle of length $\ell$ is at most $2^{O(n^{r-1}(\log n{)}^{(r-3)/(r-2)})}$. We improve this bound to $2^{O(n^{r-1}\log \log n)}$.

6 pages