$K_r$-Packings in Graphs with $t_{r-1}(n)+k$ Edges

Fix an integer $r\ge 3$. Let $K_r$ denote the complete graph on $r$ vertices and $t_{r-1}(n)$ the Turán number for $K_r$. For each integer $k$ satisfying $0\le k \le \binom{n}{2}-t_{r-1}(n)$, $\rev{ϕ_r(n,k)}$ denotes the minimum, over all $n$-vertex graphs with $t_{r-1}(n)+k$ edges, of the maximum s