3. (a) Two copies of a graph are drawn below, where bolded edges on the left copy form a given matching M. Use inspection to determine an augmenting path with respect to M , and indicate the path on the graph to the left. Use your augmenting path to get a larger matching, and indicate the new matching on the graph to the right.
(b) Let G be a graph with a perfect matching M . Let X be a subset of V (G) of even size. Prove that the number of edges of M that are in the cut induced by X is even.
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Sep 21, 2019EXPERT
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