2 problems

Let $\mathcal{P}$ be a hereditary property of ordered hypergraphs. For every constant $c>0$, suppose there exists an $N=N(c)\in\mathbb{N}$ such that $|\mathcal{P}_N|>c^N$. The orde…

Let $F$ be an $r$-uniform forest with interval chromatic number $r$. Füredi–Jiang–Kostochka–Mubayi–Verstraëte conjecture. The maximum number of edges in a vertex-ordered $r$-unifor…