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Item type:Publication, Access status: without files , Hitting cycles through prescribed vertices or edges(Society for Industrial & Applied Mathematics (SIAM), 2026-07-07); ; ; ; We prove that for every set S of vertices of a directed graph D, the maximum number of vertices in S contained in a collection of vertex-disjoint cycles in D is at least the minimum size of a set of vertices that hits all cycles containing a vertex of S. As a consequence, the directed tree-width of a directed graph is linearly bounded in its cycle-width, which improves the previously known quadratic upper bound. We further show that the corresponding statement in bidirected graphs is true and that its edge-variant holds in both undirected and directed graphs, but fails in bidirected graphs. The vertex-version in undirected graphs remains an open problem.Publicationtype: Journal Article17