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SOLVED: The parts of this exercise outline a proof of Ore's theorem. Suppose that G is a simple graph with n vertices, n ≥ 3, and deg(x) deg(y) ≥ n whenever x and y are non-adjacent vertices in G . Ore's theorem states that under these conditions, G has a Hamilton circuit.a) Show that if G does not have a Hamilton circuit, then there exists another graph H with the same vertices as G, which can be constructed by adding edges to G, such that the addition of a single edge would produce a Hamilton
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