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I know that the Hall's Theorem states that there is a matching saturating every vertex in A if and only if every subset D of A satisfies $|N(D)| \ge |D|$, and if I take the contrapositive of the "if" part, then it says: "if there is no matching that saturates every vertex of A, then $|N(D)| \lt |D|$".

My question is: suppose I have already done the XY construction and found the maximum matching M and the minimum cover C, in the case that A is not fully saturated, is there a way to find the subset D?

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