Augmenting-Path Algorithm

This is just another application of depth-first search (or breadth-first).

• Mark nodes as matched or unmatched.
• Start a search from each of the unmatched left nodes.
• Traverse red edges from left to right.
• Traverse green edges from right to left.
• Stop successfully if an unmatched right node is reached.
• Stop with failure if search terminates without finding an unmatched right node.

Running time? O((|V|+|M|)+(|V|+|E|)) = O(|V|+|E|).