  We introduce a new method to construct uncountably chromatic graphs from non
special trees and ladder systems. Answering a question of P. Erd\H{o}s and A.
Hajnal from 1985, we construct graphs of chromatic number $\omega_1$ without
uncountable $\omega$-connected subgraphs. Second, we build triangle free graphs
of chromatic number $\omega_1$ without subgraphs isomorphic to
$H_{\omega,\omega+2}$.
