5 problems

Let $r\geq 3$ be a fixed integer. For a path $P_k$ with $k$ edges, let $\mathcal{B}(P_k)$ denote its Berge hypergraph, and let $\mathrm{schex}_r(n,\mathcal{B}(P_k))$ be the strong…

Mubayi–Zhao conjecture. Given positive integers $n,r,s,t$ with $2\leqslant t<\min\{r,s\}$, there exists $n_0>0$ such that for $n>n_0$,

Higher-uniformity Berge saturation conjecture. For every $3\leq r<k$ and every $r$-uniform hypergraph $F^{(r)}$,

Let $k$ be fixed, and let $\mathcal{F}$ be any fixed finite family of graphs. Write $\operatorname{sat}_k(n,\text{Berge-}\mathcal{F})$ for the minimum number of edges in a $k$-unif…

Let $\operatorname{sat}_k(n,\text{Berge-}P_m)$ denote the minimum number of edges in a $k$-uniform hypergraph on $n$ vertices that is Berge-$P_m$-saturated, and let $a^{(k)}_m$ be…