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Apparently this is the "dual version" of Turan's Theorem. How does this theorem imply Turan's?

That $ex(n, K_{p+1}) = |E(T(n,p))|$

Where:

- $T'(n,q)$ : $q$ disjoint cliques with size as equal as possible

- $\alpha (G)$ : independence number of $G$

- $ex(n, K_{p+1})$ : max number of edges in an n-vertex graph with no $K_{p+1}$ subgraph