6 problems

Let $k$ be a positive integer, let $H$ be a $k$-graph with $n=|V(H)|$ vertices, and suppose that $n\not\equiv 0\pmod{k}$. A matching $M$ in $H$ is near-perfect if…

Illingworth–Lang–Müyesser–Parczyk–Sgueglia's conjecture. For all $k\ge 3$, if

Katona–Kierstead's conjecture. If

Let $H$ be a $3$-graph on $n$ vertices. A loose Hamiltonian cycle is a cyclic sequence of edges whose consecutive edges intersect in one vertex, nonconsecutive edges are disjoint,…

Let $H$ be an $r$-graph on $n$ vertices, and let $\delta_{r-1}^+(H)$ denote its minimum positive co-degree. A perfect matching is a collection of vertex-disjoint edges covering all…

Rödl–Ruciński–Szemerédi conjecture. This threshold function is