 Max-flow min-cut theorem

The greatest value of a feasible source-to-sink flow equals the least capacity of a source-to-sink cut. For a maximum flow, the vertices reachable from the source in the residual graph define a cut whose forward edges are saturated and whose backward edges carry zero flow.

The Max-flow Min-cut Theorem is a fundamental result in network flow theory, specifically in the context of directed (or undirected) graphs. It provides a deep relationship between two concepts: the maximum amount of flow that can be sent from a source node to a sink node in a flow network and the minimum capacity that, when removed, would disconnect the source from the sink.