I'm stuck trying to prove that If all edges in a network have distinct capacities, then the min-cut is unique. I'd like to know if there is some proof that doesn't involve going through F&F algorithm, or designing one. Instead, I tried proving it by contradiction, assuming the existence of two different cuts with equal capacities (and both minimums) but I don't know how to arrive to a contradiction.
2026-03-26 17:32:18.1774546338
If all edges in a network have distinct capacities, then the min-cut is unique
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There is the following counterexample for the claim you trying to prove.