  In a vertex-colored graph $G = (V, E)$, a subset $S \subseteq V$ is said to
be consistent if every vertex has a nearest neighbor in $S$ with the same
color. The problem of computing a minimum cardinality consistent subset of a
graph is known to be NP-hard. On the positive side, Dey et al. (FCT 2021) show
that this problem is solvable in polynomial time when input graphs are
restricted to bi-colored trees. In this paper, we give a polynomial-time
algorithm for this problem on $k$-colored trees with fixed $k$.
