2 problems

Let $T$ be an $n$-vertex tournament. An inversion reverses all edges whose endpoints lie in a specified vertex set, and ${\rm inv}_k(T)$ is the minimum length of a sequence of inve…

Let $F \neq K_2$ be a non-empty graph with vertex set $\{1,\ldots,m\}$, and let $\alpha_1,\ldots,\alpha_m \in (0,1)$ satisfy … Write $\mathcal{P}(F,\alpha_1,\ldots,\alpha_m)$ for t…