Is there an efficient algorithm to find all the maximum matching in any tree?

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A matching in a graph (G) is a set of mutually non-adjacent edges of (G). A maximum matching is a matching maxima cardinallity. A tree is an acyclic connected graph.

Is there an efficient algorithm to find all the maximum matching in any tree?

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Hint:

  • How many maximum matchings there might be?

I hope this helps $\ddot\smile$