Maximum flow with vertex capacities
= Maximum flow with vertex capacities
The <maximum flow problem> with internal <vertex capacities> reduces to the usual edge-capacitated problem by splitting each constrained vertex into input and output copies. The connecting edge carries its entire through-flow. Feasible flows correspond under this construction, preserving the source-to-sink value; the <Ford-Fulkerson algorithm> and <max-flow min-cut theorem> therefore apply to the transformed network.