5 problems

Supersaturation conjecture. There exist $c_1,c_2>0$ such that

Let $K\colon\mathbb{N}\rightarrow\mathbb{R}$ be the smallest function such that every $r$-bounded hypergraph $\mathcal{H}$ on a finite vertex set $V$ admits a cover…

Interpolation conjecture. For $\frac{3}{2}<x\leq 4$,

Let $H$ be an $r$-graph. For $\alpha>0$, call $H$ Erdős–Simonovits $\alpha$-good for a function $m=m(n)$ if there exist positive constants $C$ and $k_0$ such that, whenever…

Let $H$ be a bipartite graph, with $e(H)$ edges, and let $\operatorname{ex}(n,H)$ denote its extremal number. Refined Erd s–Simonovits conjecture. There exist constants $C>0$,…