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I was studying flow networks and intersection/union of min cuts in such networks, Im trying to prove a theory that says if the intersection of two min cuts A, B had s in it (meaning (A)intersection(B)={s}) and only s that {s} by itself is also a min-cut. Now im trying to prove this by saying that every edge from s considering it's a min-cut cutting edge must be saturated, I think i've managed to prove it for the situation where s has only 1 or 2 neighbours but I don't know how to continue from there.

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