Induced Complete $h$-partite Graphs in Dense Clique-less Graphs

Abstract

It is proven that for every fixed $h$, $a$ and $b$, a graph with $n$ vertices and minimum degree at least ${h-1 \over h}n$, which contains no copy of $K_b$ (the complete graph with $b$ vertices), contains at least $(1-o(1)){n \over ha}$ vertex disjoint induced copies of the complete $h$-partite graph with $a$ vertices in each color class.