In combinatorial mathematics, Hall's marriage theorem, or simply Hall's Theorem, gives a necessary and sufficient condition for being able to select a distinct element from each of a collection of finite sets. It was proved by Philip Hall (1935).
Read more about Hall's Marriage Theorem: Definitions and Statement of The Theorem, Discussion and Examples, Graph Theoretic Formulation, Proof of The Graph Theoretic Version, Marshall Hall Jr. Variant, Applications, Marriage Condition Does Not Extend, Logical Equivalences
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