Many Cliques with Few Edges

Recently Cutler and Radcliffe proved that the graph on $n$ vertices with maximum degree at most $r$ having cliques is a disjoint union of $\lfloor n/(r+1)\rfloor$ size $r+1$ together clique remainder vertices. It very natural also to consider this question when limiting resource edges rather than In paper we prove among graphs $m$ $r$, has least two $\bigl\lfloor m \bigm/\binom{r+1}{2} \bigr\rfloor$ colex using edges.