Suppose that, in addition to edge capacities, a flow network has vertex capacities. That is each vertex vv has a limit l(v)l(v) on how much flow can pass though vv. Show how to transform a flow network G = (V, E)G=(V,E) with vertex capacities into an equivalent flow network G' = (V', E')G ′ =(V ′ ,E ′ ) without vertex capacities, such that a maximum flow in G'G ′ has the same value as a maximum flow in GG. How many vertices and edges does G'G ′ have?
