A characterization of middle graphs and a matroid associated with middle graphs of hypergraphs
We prove that a rank Dowling geometry of a group is partition representable if and only if is a Frobenius complement. This implies that Dowling group geometries are secret-sharing if and only if they are multilinearly representable.
The aim of this paper is to generalize several basic results from transversal theory, primarily the theorem of Edmonds and Fulkerson.