Construction

1. Find max matching. 2. Let U = unmatched left vertices. 3. Alternating BFS from U: even level via matching, odd via non-matching. 4. Cover = (left \ visited) ∪ (right ∩ visited).

Advertisement

Complexity

Max matching: O(E·√V). Cover extraction: O(V+E). Total: O(E·√V).

Advertisement

Independent set

Complement of vertex cover is independent set. Bipartite max indep set = V - min vertex cover.

Applications

Job scheduling. Facility placement. Any bipartite conflict minimization.