2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168326If we fix a spanning subgraph $H$ of a graph $G$, we can define a chromatic number of $H$ with respect to $G$ and we show that it coincides with the chromatic number of a double covering of $G$ with co-support $H$. We also find a few estimations for the chromatic numbers of $H$ with respect to $G$.10 pagesCombinatorics05C15text