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Prove that x(G) x (G) n(G), use this to prove that x (G) + x(G) 2n(G), and provide a construction achieving these bounds whenever

 

Prove that x(G) x (G) n(G), use this to prove that x (G) + x(G) 2n(G), and provide a construction achieving these bounds whenever n(G) is an integer.

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