Leírás
Tomon István: The extremal number of tight cycles
Abstract: A tight cycle in an $r$-uniform hypergraph $\mathcal{H}$ is a sequence of $\ell\geq r+1$ vertices $x_1,\dots,x_{\ell}$ such that all $r$-tuples $\{x_{i},x_{i+1},\dots,x_{i+r-1}\}$ (with subscripts modulo $\ell$) are edges of $\mathcal{H}$.
An old problem of V. Sos, also posed independently by J. Verstraete, asks for the maximum number of edges in an $r$-uniform hypergraph on $n$ vertices which has no tight cycle. Although this is a very basic question, until recently, no good upper bounds were known for this problem for $r\geq 3$. In my talk, I will present a brief outline of the proof of the upper bound $n^{r-1+o(1)}$, which is tight up to the $o(1)$ error term. This is based on a joint work with Benny Sudakov.
https://zoom.us/j/99077837563?pwd=ejdJcUxOQVpxNk53NldiR3VKVkM3dz09