Question: A matching is maximal if it does not leave any free edge. Let M be a maximal matching and M * be a maximum matching.

A matching is maximal if it does not leave any free

A matching is maximal if it does not leave any free edge. Let M be a maximal matching and M * be a maximum matching. Prove that |M| greaterthanorequalto 1/2 middot |M*|. Conclude an O (E) time 2-approximation algorithm for computing the maximum matching, an O (E) time algorithm that computes a matching of size at least 1/2 of the maximum matching

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