Sufficiency Conditions for the Existence of Transversals
E. C. Milner, Saharon Shelah · Canadian Journal of Mathematics · 1974
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 [9]. The best known result of this kind is the following theorem.