## Saturated vertices and Maximum matchings

Let \(S\) be a set of vertices saturated by a matching \(M\) in a graph \(G\).

Prove that some maximum matching also saturates all of \(S\).

Must the statement be true for every maximum matching ?

Let \(S\) be a set of vertices saturated by a matching \(M\) in a graph \(G\).

Prove that some maximum matching also saturates all of \(S\).

Must the statement be true for every maximum matching ?