6 problems

Let $K^s_t$ be the complete $s$-uniform hypergraph on $t$ vertices, and let $\mathrm{sat}(n,K^s_t)$ denote its saturation number on $n$ vertices. Saturation-number conjecture. For…

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

Pikhurko's conjecture. For every $r$-graph $F$, the limit

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…

Let $S_n(p,q)$ be the minimum number of edges in an $n\times n$ bipartite graph such that adding any new edge between its two classes creates a copy of $K_{p,q}$. Let…