4 problems

Let $\theta_{\operatorname{STS}}$ denote the minimum codegree threshold for Steiner triple systems, and let $\theta_{\operatorname{STS}}^*$ denote the corresponding fractional thre…

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 integers $k\geq 2$, let $K_{k+1}^k$ be the complete $k$-graph on $k+1$ vertices. For a $k$-graph $H$, let $\delta_{k-1}(H)$ be its minimum $(k-1)$-degree, and let…

Let $t_2^3(n,K_4^3-e)$ be the smallest integer $d$ such that every 3-uniform hypergraph on $n$ vertices with minimum 2-degree at least $d$ contains a spanning collection of vertex-…