Question: 1. Give an algorithm that finds a maximal for inclusion matching M, in polynomial time. 2. Consider a set W that contains the 2|M| vertices

1. Give an algorithm that finds a maximal for inclusion matching

1. Give an algorithm that finds a maximal for inclusion matching M, in polynomial time.

2. Consider a set W that contains the 2|M| vertices of a maximal matching M. Show that this set is a vertex cover in the graph.

3. Let vc be the size of the smallest vertex cover in the graph. Show that for any matching M, |M| vc

Question 3: Recall that a matching is a collection of edges, no two of which share an endpoint. A matching M = {ei} is maximal for inclusion if there is no other matching M' so that M CM' and M #M'. Question 3: Recall that a matching is a collection of edges, no two of which share an endpoint. A matching M = {ei} is maximal for inclusion if there is no other matching M' so that M CM' and M #M

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