3 problems

Stability characterization conjecture. For every integer $p\ge 1$,

Let $H=(V,E)$ be an $r$-uniform hypergraph, meaning that every edge has cardinality $r$. A hypergraph is vertex-$k$-maximal if every subhypergraph has vertex-connectivity at most…

Let $\mathcal{F}_n$ be the family of graphs on $n$ vertices, let $\mathcal{V}_n^k$ denote the graphs in $\mathcal{F}_n$ with vertex connectivity at most $k$, and let $n,k$ be posit…