10 problems

Let $H$ be a $k$-uniform hypergraph, and for $1\leq \ell<k$ let $\delta_\ell(H)$ denote its minimum $\ell$-degree. Define $m_{\ell,k}$ as the infimum of those $c\in[0,1]$ such that…

Matching existence conjecture. If this conjecture holds for $6\leq k\leq 16$, then

Alon et al.'s fractional matching threshold conjecture. For all $1\leq d\leq k-1$,

Equality conjecture. For all $k>j\geqslant 1$,

Hamilton vicinity threshold conjecture.

Polcyn–Reiher–Rödl–Ruciński–Schacht–Schülke conjecture.

Hàn–Person–Schacht–Kühn–Osthus–Townsend conjecture. The asymptotic $l$-degree threshold for a perfect matching in a $k$-graph with $n$ vertices is

Perfect matching threshold conjecture. For general $d$, the minimum $d$-degree threshold that guarantees a perfect matching is

Let $h^l_d(k,n)$ denote the minimum integer $m$ such that every $k$-uniform hypergraph $\mathcal{H}$ on $n$ vertices with minimum $d$-degree $\delta_d(\mathcal{H})\ge m$ contains a…

Let $k,ll in \mathbb N$ satisfy … Let $H$ be a $k$-uniform hypergraph on $n\geq n_0$ vertices, where $n_0\in\mathbb N$ and $k$ divides $n$. Write $\delta_\ell(H)$ for the minimum…