All Questions

Let $k\in\mathbb N$. Given a finite graph with two subsets of vertices $X$ and $Y$, Menger's Theorem gives a criterion for when there are $k$ pairwise disjoint paths starting in $X$ and ending in $Y$. ...

Let $G$ be a graph and let $A_1, A_2 \subseteq V(G)$ be disjoint sets of vertices. Let us call $(A_1, A_2)$ independent if there exist vertex-disjoint trees $T_1, T_2 \subseteq G$ within $G$ which ...