Hall's Marriage Theorem, Its Applications and History

Abstract

Hall's marriage theorem is one of the basic results in combinatorics. The article focuses on some classical as well as less familiar applications.

It describes the early history of the theorem and related results, which is connected not only with the name of Philip Hall, but also other excellent mathematicians of the first half of the 20th century.

Keywords

• combinatorics
• Hall's marriage theorem
• matching in bipartite graphs
• system of distinct representatives
• history