6 problems

Illingworth–Lang–Müyesser–Parczyk–Sgueglia's conjecture. If $H$ has minimum codegree at least $n/k$, then $H$ has a spanning tight component.

Let $H$ be an $r$-uniform hypergraph on $n$ vertices containing no $(k+1)$-connected subgraph. Hypergraph Mader conjecture. For all sufficiently large $n$, … This proposed extensio…

Let $G$ be a $k$-graph on $n$ vertices, and let $\delta_{k-1}(G)$ denote its minimum $(k-1)$-degree. Minimum-codegree spanning-component conjecture. If … then $G$ contains a spanni…

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 $k$-graph on $n$ vertices. Write $\delta_1(G)$ for its minimum vertex degree, the minimum number of edges containing any one vertex. Spanning-component conjecture. If…

Tightly connected hypergraph conjecture. For every $r\geq 3$, every $r$-coloring of $K_n^r$ contains a monochromatic tightly connected subgraph covering all vertices of $K_n^r$.