##### ###### ##### ### # # ### # # ###### ## ## ## ## ## ## ## # # # # # ## ##### #### ##### # # # # # # # #### ## # ## ## ## ## # # # # # ## ## # ###### ## ### # ### # ######
##### ###### ##### ### # # ### # # ###### ## ## ## ## ## ## ## # # # # # ## ##### #### ##### # # # # # # # #### ## # ## ## ## ## # # # # # ## ## # ###### ## ### # ### # ######
(Partitioning the graph)
A cut divides the nodes into two sets and , where the source is in and the sink is in . The capacity of the cut is the sum of capacities of edges going from to . Edges from to do not count toward cut capacity.
Only forward edges (from to ) matter. Every flow from source to sink must cross the cut. So the flow value is at most the cut capacity. This is true for every cut.
