So I know that these are both true, but if I change the values would they still be true? Do these statements hold for any value?
A) Suppose f is a flow of value 50 from s to t in a flow network G. The capacity of the minimum s-t cut in G is equal to 50.
Suppose we were using 100 or maybe 75 instead of 50. Is this still true?
B) Suppose f is a flow of value 100 from s to t in a flow network G and there is an s-t cut of capacity 100. Then there are no s --> t paths in the residual graph Gf.
If we use 80, 60, 20 and so on is this still true? What about for odd numbers?