is only 1. This is in contrast to the situation in bipartite graphs, in which a perfect fractional matching implies the existence of a perfect matching. Design-theoretic aspects Dual affine planes can be viewed as a point residue of a projective plane, a 1-design, and, more classically, as a tactical configuration. Since they are not pairwise balanced designs (PBDs), they have not been studied extensively from the design-theoretic viewpoint. However, tactical configurations are central topics in geometry, especially finite geometry. History According to , the term "tactical configuration" appears to be due to E. H. Moore in 1896. For the history of dual configurations, see Duality (projective geometry)#History. Notes References Hypergraphs Projective geometry