  Let $\mathcal{G}$ be the set of all connected graphs on vertex set $[n]$.
Define the partial ordering $<$ on $\mathcal{G}$ as follows: for $G,H\in
\mathcal{G}$ let $G<H$ if $E(G)\subset E(H)$. The poset $(\mathcal{G},<)$ is
graded, each level containing the connected graphs with the same number of
edges. We prove that $(\mathcal{G},<)$ has the Sperner property, namely that
the largest antichain of $(\mathcal{G},<)$ is equal to its largest sized level.
