SOLVED
Let $r\geq 2$ and $m\geq 1$. Every graph with $rm$ vertices and minimum degree at least $m(r-1)$ contains $m$ vertex disjoint copies of $K_r$.
When $r=2$ this follows from
Dirac's theorem. Corrádi and Hajnal
[CoHa63] proved this when $r=3$. Hajnal and Szemerédi
[HaSz70] proved this for all $r\geq 4$.
