Q82b

Let $s$ and $t$ be two vertices in a undirected graph $G=(V,E)$ having distinct positive edge weights. Let $[X,Y]$ be a partition of $V$ such that $s \in X$ and $t \in Y$. Consider the edge $e$ having the minimum weight amongst all those edges that have one vertex in $X$ and one vertex in $Y$. Let the weight of an edge $e$ denote the congestion on that edge. The congestion on a path is defined to be the maximum of the congestions on the edges of the path. We wish to find the path from $s$ to $t$ having minimum congestion. Which of the following paths is always such a path of minimum congestion?