Sufficiency Conditions for the Existence of Transversals

Abstract

A transversal of a family of non-empty sets is a 1-1 map such that φ ( v ) ∊ F v ( 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.