1. Prove that K[n/2],[n/2] is the only sharpness example for Mantel's Theorem. That is, show that: if G is a triangle-free n-vertex simple graph and e(G) = [n²/4], then G≈ K[n/2], [n/2]. Hint: Follow the proof of Mantel's Theorem. Knowing e(G) allows you to conclude that some inequalities must be equalities.

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