arXiv · 1703.10963
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 $2^{O( n^{r-1} \log \log n) }$.
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Jie Han, Yoshiharu Kohayakawa. 2017-03-31. On hypergraphs without loose cycles. https://arxiv.org/abs/1703.10963
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