3 problems

Chernyshev–Rauch–Rautenbach conjecture. If $G$ has fewer than $3n-6$ edges, then $G$ has a forest cut.

$\alpha$-FC conjecture. If $G$ has no forest cut, then

Let $G$ be a finite, simple, undirected graph of order $n$, and call a vertex set a forest cut if it is a vertex cut whose induced subgraph is a forest. Forest-cut conjecture. If…