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4. (10 pts) Show that if an n-vertex graph has more than 12(n - 1) (n - 2) edges, then it must be connected. (Hint:

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4. (10 pts) Show that if an n-vertex graph has more than 12(n - 1) (n - 2) edges, then it must be connected. (Hint: The most edges possible in a disconnected graph will occur when there are two components, each complete Subgraphs.)

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