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Sufficiency Conditions for the Existence of Transversals

Published online by Cambridge University Press:  20 November 2018

E. C. Milner
University of Calgary, Calgary, Alberta
S. Shelah
University of Jerusalem, Jerusalem, Israel
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A transversal of a family of non-empty sets is a 1-1 map

such that φ(v) ∊ Fv (vI) . 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.

Research Article
Copyright © Canadian Mathematical Society 1974


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