  We introduce a new type of examples of bounded degree acyclic Borel graphs
and study their combinatorial properties in the context of descriptive
combinatorics, using a generalization of the determinacy method of Marks. The
motivation for the construction comes from the adaptation of this method to the
LOCAL model of distributed computing. Our approach unifies the previous results
in the area, as well as produces new ones. In particular, we show that for
$\Delta>2$ it is impossible to give a simple characterization of acyclic
$\Delta$-regular Borel graphs with Borel chromatic number at most $\Delta$:
such graphs form a $\mathbf{\Sigma}^1_2$-complete set. This implies a strong
failure of Brooks'-like theorems in the Borel context.
