Let f‾ denote the flow returned by the Ford-Fulkerson Algorithm
Let an s-t cut (A*,B*) for which v(f- = c(A*,B*)
Thus f- has the maximum value of any flow, and (A*,B*) has the minimum capacity of any s-t cut in G.
The flow f- returned by the Ford-Fulkerson Algorithm is a maximum flow
Given a flow f of maximum value, an s-t cut can be computed of minimum capacity can be computed in O(m) time
In every flow network, the maximum value of an s-t flow is equal to the minimum capacity of an s-t cut
If all capacities in the flow network are integers, then there is a maximum flow f for which every flow value f(e) is an integer