Chapter 7.2: Maximum Flows and Minimum Cuts in a Network

Consider dividing the nodes of the graph into two sets A and B, so that s is in A and t is in B. We say that an s-t cut is a partition (A,B) of the vertex set V so that s is in A and t is in B. The capacity of a cut (A,B), denoted c(A,B), is the sum of the capacities of all edges out of A.

Let f be any s-t flow and (A,B) any s-t cut. Then v(f)=f_out(A)-f_in(A)≤c(A,B).

If f is an s-t flow such that there is no s-t path in the residual graph G_f, then there is an s-t cut (A*,B*) in G for which v(f)=c(A*,B*). Consequently, f has the maximum value of any flow in G, and (A*,B*) has the minimum capacity of any s-t cut in G.

I would rate this section a 1 because I really don't understand any of it. There is only one picture and it is terrible. I feel like this topic relies heavily on visualizing the problem so I really haven't taken much from this section.