10 problems

Let $H$ be an $n$-vertex $k$-uniform hypergraph, and let … vertices. For integers $k\ge 3$ and $k/2<\ell<k$ with $k\not\equiv 0 \pmod{k-\ell}$, assume that $n$ is sufficiently larg…

For $k\geq 3$, let $H_1$ and $H_2$ be $k$-graphs on the same $n$-vertex set, and let $T_k$ denote the generalised triangle. Write $\delta(H_i)$ for the minimum codegree of $H_i$. T…

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

Let $n_0\in\mathbb{N}$ and $C\in\mathbb{R}$ be constants. For every $n\geq n_0$ satisfying $n\equiv 1,3\pmod{6}$, let $\mathcal{H}=\{H_1,\dots,H_{n(n-1)/6}\}$ be a family of $3$-un…

Let $H$ be a $3$-uniform hypergraph, let $|H|$ denote its number of vertices, and let $[?]$ be its minimum codegree. A cycle decomposition is a decomposition of the edges of $H$ in…

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…

Falgas-Ravry–Zhao's conjecture. The gap between the known lower and upper bounds for $c_2(n,K_4^-)$ can be closed; equivalently, the exact minimum codegree threshold for $K_4^-$-co…

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-…

Let $k>l\ge 1$, and let $t_l^k(n,K_k^k)$ be the smallest integer $d$ such that every $k$-uniform hypergraph on $n$ vertices with minimum $l$-degree at least $d$ contains a perfect…