Widest path problem
= Widest path problem
{title2=$\max_{P:s\leadsto t}\min_{e\in P}w(e)$}
{wiki}
Find a <graph path> whose least <edge weight> is as large as possible. In a connected <undirected graph>, use the unique route in a <maximum spanning tree>. Deleting a least-weight <edge> on that route gives a separating <cut of a graph>; a heavier crossing <edge> would improve the tree's total weight, so every competing route contains an <edge> no heavier than the deleted one. This proves the bottleneck optimum without assuming distinct weights.