The ACO Seminar (2022–2023)

Given $r$-uniform hypergraphs $G$ and $H$ the Turan number ex$(G, H)$ is the maximum number of edges in an $H$-free subgraph of $G$. We study the typical value of ex$(G, H)$ when $G=G_{n,p}^{(r)}$, the Erdos-Renyi random $r$-uniform hypergraph, and $H=C_{2\ell}^{(r)}$, the $r$-uniform linear cycle of length $2\ell$. The case of graphs ($r=2$) is a longstanding open problem that has been investigated by many researchers. We examine ex$(G_{n,p}^{(r)}, C_{2\ell}^{(r)})$ for higher uniformities. This is joint work with Dhruv Mubayi and Gwen McKinley.