Question: In the Smallest Maximal Matching problem, you are given an undirected graph G, you want to find a matching (that is, a subset of edges

In the Smallest Maximal Matching problem, you are given an undirected graph G, you want to find a matching (that is, a subset of edges M such that no two edges share an endpoint). M must be maximal, in that you cannot add any one edge to M and have it still be a matching. You want to find the maximal matching with the fewest possible edges. Give a 2-approximation algorithm for this problem, and analyze the approximation factor.

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