  We study colorings of the hyperbolic plane, analogously to the
Hadwiger-Nelson problem for the Euclidean plane. The idea is to color points
using the minimum number of colors such that no two points at distance exactly
$d$ are of the same color. The problem depends on $d$ and, following a strategy
of Kloeckner, we show linear upper bounds on the necessary number of colors. In
parallel, we study the same problem on $q$-regular trees and show analogous
results. For both settings, we also consider a variant which consists in
replacing $d$ with an interval of distances.
