For any flow network G = (V, E) and any cut (S, T) of G, we define the
cardinality of cut (S, T) as |{(u, v) ∈ E | u ∈ S ∧ v ∈ T}|.
Consider the following decision problem: Given an integer k and a flow network G with integer
edge capacities, does G have a minimum-capacity cut with cardinality at most k? Prove that this
decision problem can be solved in polynomial time.
Hint: Apply a suitable transformation to the edge capacities of G