## maximum flow and minimum cut

Find the maximum flow and minimum cut for the following network the capacities are marked.

the minimum cut is $(X, \overline{X})$ where $X = \{s, x\}$ and $\overline{X} = \{y,z,u,v,w,t\}$ so the capacity of the minimum cut is $c(s,u) + c(x,y) = 4 + 3 = 7$.