5 problems

Asymptotic extremal conjecture for ordered 3-uniform tight paths. The constructions described in the source are asymptotically optimal:

Let $H$ be an $n$-vertex $3$-graph, and let $[?]$ denote its minimum codegree, the minimum number of common neighbours over all pairs of vertices. A collection of tight paths is ve…

For $n \geq r \geq 2$ and $k \geq 1$, let $P_k^r$ be the tight $k$-path in an $r$-uniform hypergraph, and let ${\rm ex}(n,P_k^r)$ denote the maximum number of edges in an $n$-verte…

For integers $2\le k < s < n$ and $2\le t\le {s\choose k}$, let $r_k(s,t;P_n)$ be the minimum $N$ such that every red/blue coloring of the $k$-sets of $[N]$ contains a monochromati…

Extremal conjecture for tight paths and cycles. For any $\ell$, every $n$-vertex $k$-graph with more than