2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/130154We consider vertex coloring of an acyclic digraph $\Gdag$ in such a way that two vertices which have a common ancestor in $\Gdag$ receive distinct colors. Such colorings arise in a natural way when bounding space for various genetic data for efficient analysis. We discuss the corresponding {\em down-chromatic number} and derive an upper bound as a function of $D(\Gdag)$, the maximum number of descendants of a given vertex, and the degeneracy of the corresponding hypergraph. Finally we determine an asymptotically tight upper bound of the down-chromatic number in terms of the number of vertices of $\Gdag$ and $D(\Gdag)$.15 pagesCombinatorics05C15, 05C20text