  Geschke proved that there is clopen graph on $2^\omega$ which is 3-saturated,
but the clopen graphs on $2^\omega$ do not even have infinite subgraphs that
are 4-saturated; however there is $F_\sigma$ graph that is
$\omega_1$-saturated. It turns out that there is no closed graph on $2^\omega$
which is $\omega$-saturated. In this note we complete this picture by proving
that for every $n$ there is an $n$-saturated closed graph on the Cantor space
$2^\omega$. The key lemma is based on probabilistic argument. The final
construction is an inverse limit of finite graphs.
