Published online by Cambridge University Press: 20 November 2018
A transversal of a family of non-empty sets is a 1-1 map
such that φ(v) ∊ Fv (v ∊ I) . A number of problems in combinatorial mathematics reduce to the question of whether or not a certain family of sets has a transversal. An up-to-date account of this theory is to be found in the book by Mirsky . The best known result of this kind is the following theorem.