Question: In Theorem is it true that if there is an augmenting path P with edge set E(P) for a matching M, then M?E(P) is a larger matching than M?
Theorem: A matching M in a graph is of maximum size if and only if M has no augmenting path. Further, if a matching M has an augmenting path P with edge set E(P), then we can in M ∩ E(P) from M and adding in the edges of E(P) - M. create a larger matching by deleting the edges.