  Given an integer $r\gs 2$, an important theorem first proved by B.
Andr\'asfai, P. Erd\H{o}s, and V. T. S\'os states that any $K_{r+1}$--free
graph on $n$ vertices whose minimum degree is greater than $(3r-4)n/(3r-1)$ is
$r$--colourable, and determines the graphs that are extremal in this context.
The purpose of this note is to give an alternative proof of this result using a
different idea.
