Let G be a bipartite graph with bipartition (A, B), satisfying ∣A∣ = ∣B∣. Suppose that G is connected and that every vertex in B has a different degree. Prove that G contains a perfect matching.
So I understand the whole idea that for a graph to be bipartite, it must have every edge going from one side to another. And I understand that for the graph to have a perfect matching, it must have every vertex belonging to an edge.
But is there a proper way to prove that this particular one does. If so, what would that method be?