Hall's Marriage Theorem
Hall's Marriage Theorem is a concept in combinatorics that addresses the problem of matching elements from two sets. Specifically, it states that a perfect matching exists between a set of women and a set of men if, for every subset of women, the number of men who are willing to marry them is at least as large as the number of women in that subset.
This theorem is often visualized using bipartite graphs, where one set represents women and the other represents men. If the conditions of the theorem are met, it guarantees that all women can be paired with men, ensuring that everyone finds a partner.