2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79622Konig's theorem states that the covering number and the matching number of a bipartite graph are equal. We prove a generalisation of this result, in which each point in one side of the graph is replaced by a subtree of a given tree. The proof uses a recent extension of Hall's theorem to families of hypergraphs, by the first author and P. Haxell.6 pages, no figures. Submitted to Combinatorica. Minor mistakes in the proofs in v1 were correctedCombinatoricstext