11 problems

Let $G$ be a $3$-graph on $n$ vertices, and let $\delta_2(G)$ denote its minimum codegree. Define the $4$-graph $H$ on $V(G)$ by making a $4$-set an edge whenever it spans a tetrah…

Let $G$ be a graph. Its square $G^2$ is obtained by joining distinct vertices that are connected by a two-edge path in $G$. Let $\operatorname{\Delta}(G)$ be the maximum degree,…

Let $G$ be a graph, with maximum degree $\operatorname{\Delta}(G)$, maximum codegree $\operatorname{\Delta_2}(G)$, and chromatic number $\chi(G)$. Vu's sharpened conjecture. There…

Let $G$ be a graph. Write $\operatorname{\Delta_2}(G)$ for its maximum codegree and $\operatorname{\Delta}(G)$ for its maximum degree. Vu's conjecture. Fix…

There exists an integer $n_0$ such that for all $n\geq n_0$, the following holds. Let $\mathcal{C}$ be a $3$-graph consisting of vertex-disjoint loose cycles…

Higher-dimensional spanning-sphere conjecture. If $\mathcal{H}$ comprises a single tight component and every set $Z$ of $r-1$ vertices contained in an edge of $\mathcal{H}$ is cont…

Spanning-sphere conjecture. Every such $\mathcal{H}$ with

Mycroft's constant-error conjecture. There exists a constant $C=C(F)$ such that the error terms in $$ can be replaced by $C$.

Lattice join projection conjecture. If

Codegree decomposition conjecture. If

Dickenstein–Nill rational codegree conjecture. If