Hall’s Theorem and Condition for Bipartite Matchings | Graph Theory, Hall’s Marriage Theorem

What are Hall’s Theorem and Hall’s Condition for bipartite matchings in graph theory? Also sometimes called Hall’s marriage theorem, we’ll be going it in today’s video graph theory lesson! A bipartite graph with partite sets U and W, where U has as many or fewer vertices than W, satisfies Hall’s condition if, for every subset S of U, S has as many or fewer vertices than it has neighbors (note that all of S’s neighbors are in W, since this is a bipartite graph). Now let G be a bipartite graph with partite sets U and W, where |U| is less than or equal to |W|. Hall’s theorem states that G contains a matching that covers U if and only if G satisfies Hall’s condition. Lesson on matchings: Proof of Hall’s theorem: I hope you find this video helpful, and be sure to ask any questions down in the comments! WRATH OF MATH ◆ Supp