2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/106157We show that the problem of the existence of universal graphs with specified forbidden subgraphs can be systematically reduced to certain critical cases by a simple pruning technique which simplifies the underlying structure of the forbidden graphs, viewed as trees of blocks. As an application, we characterize the trees T for which a universal countable T-free graph exists.LogicCombinatoricstext