Police Chase - Walkthrough

Example: $5$ nodes, edges ($1$,$2$), ($1$,$3$), ($2$,$4$), ($3$,$4$), ($4$,$5$). Max flow is $2$.

This means there are $2$ edge-disjoint paths from source to sink. The algorithm finds paths $1 \to 2 \to 4 \to 5$ and $1 \to 3 \to 4 \to 5$. Min-cut must have $2$ edges to disconnect all paths. BFS from $1$ on the residual graph reaches nodes $1$, $2$, $3$. Nodes $4$ and $5$ are not reachable. Edges crossing the cut: ($2$,$4$) and ($3$,$4$). 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.