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The edit distance from a large complete $p$-partite graph to the Turán graph

For the first inequality: \begin{align*} \sum(|V_i| -\frac{n}{p})^2 &= \sum\left(|V_i|^2 - 2\frac np |V_i| + \frac{n^2}{p^2}\right) \\ &= \left(\sum |V_i|^2\right) - 2n^2/p + n^2/p \\ &= 2\...
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Gentle(-er) Introduction to Erdős–Bollobás's solution to Ramsey–Turán Type Problem

I found an excellent account of this problem in the thesis of John Lenz: xtremal graph theory: Ramsey-Turán numbers, chromatic thresholds, and minors Lenz, John E.
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