  The components of the graphs $D(n, q)$ provide the best-known general lower
bound for the number of edges in a graph with $n$ vertices and no cycles of
length less than $g$. In this paper, we give a new, short, and simpler proof of
the fact that the length of the shortest cycle appearing in $D(n, q)$ is $n +
5$ when $n$ is odd, and $n + 4$ when $n$ is even.
