On n-saturated Closed Graphs

Geschke proved in [2] that there is a clopen graph on \(2^\omega \) which 3-saturated, but the graphs do not even have infinite subgraphs are 4-saturated; however \(F_\sigma \(\omega _1\)-saturated. It turns out no closed \)-saturated, see [3]. In this note we complete picture by proving for every \(n\in {\mathbb {N}}\) an n-saturated Cantor space \). The key lemma based probabilistic argument. final construction inverse limit of finite graphs.