Unit Capacity Dinic

Dinic on a bipartite matching network: unit capacities, and every vertex other than $s$ and $t$ has in-degree $1$ or out-degree $1$ . The textbook bound is $O(V^2E)$ . What is the real one?

$O(E \log V)$ . The unit-capacity structure caps the number of phases at $O(\log V)$ , which is exactly the capacity scaling bound.

$O(E\sqrt{V})$ . The unit-capacity structure caps the number of phases at $O(\sqrt{V})$ , which is exactly the Hopcroft-Karp bound.

$O(V^2E)$ . Unit capacities cap nothing extra, so the phase count stays at $O(V)$ , which is exactly the textbook Dinic bound.

$O(VE)$ . Unit capacities cap nothing extra, so the phase count stays at $O(V)$ , which is exactly the Kuhn's algorithm bound.