For large n and any k ≤ n/4, the maximum number of edges in an n-vertex graph with no k+1 disjoint K4's is asymptotically Ξ(n,k), a piecewise quadratic with five regimes.
On the size of graphs with complete factors
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Density Hajnal--Szemer\'{e}di theorem for cliques of size four
For large n and any k ≤ n/4, the maximum number of edges in an n-vertex graph with no k+1 disjoint K4's is asymptotically Ξ(n,k), a piecewise quadratic with five regimes.