Question: This is a question in my practice test I've been wondering about, thank you! Let G be a graph and Z Q V(G). Show that

This is a question in my practice test I've been wondering about, thank you!

Let G be a graph and Z Q V(G). Show that the following are equivalent: (i) G has a matching covering Z (ii) for every X E V(G) there are at most |X I odd components 0 of G\\X such that V(C') E Z. [Hint: add extra vertices appropriately.]

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