Let s and t be two vertices in a undirected graph G=(V,E) having distinct positive edge weights.
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∈X and t∈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?
a path from s to t in the minimum weighted spanning tree
a weighted shortest path from s to t
an Euler walk from s to t
a Hamiltonian path from s to t