Algorithms: max flow problem and s-t minimum cut

Let G be an input graph to the max flow problem. Let A be a minimum s-t cut in the graph. Suppose we add 1 to the capacity of every edge in the graph. Is it ne开发者_如何转开发cessarily true that A is still a minimum cut? If so, prove it, if not give a counterexample

[Note: I think the answer is no, not necessarily, but I cannot come up with a counterexample] Please note that this is a homework question, I am looking for a hint or any help I can get :)

With user57368 remark it is easy to construct simple counterexamples.

E.g. V={A,B,C,D}, E={(A,B,2.5), (B,D,1), (C,D,1)}. Minimal cut is {(B,D), (C,D)} with weight 2.

If you add weight 1 to every edge, you get E2={(A,B,3.5), (B,D,2), (C,D,2)}. Here is minimal cut {(A,B)} with weight 3.5.