Example: nodes, edges (,), (,), (,), (,), (,). Max flow is .
This means there are edge-disjoint paths from source to sink. The algorithm finds paths and . Min-cut must have edges to disconnect all paths. BFS from on the residual graph reaches nodes , , . Nodes and are not reachable. Edges crossing the cut: (,) and (,). Block those two roads and the criminal cannot escape. The algorithm found the minimum set. You can verify no smaller set disconnects source from sink.