What is an 'Augmenting Path' in matching?

Approach: Define a path that alternates between unmatched and matched edges.

A path that starts and ends at unmatched vertices and alternates between edges not in the matching and edges in the matching. Finding one allows increasing the matching size.

Follow-up: How is it used in the Hopcroft-Karp algorithm?

Key concepts: bipartite matching, berge's theorem.