A graph G is a k-regular graph if all the vertices of G has the same degree k. For example, Kn is a (n-1)-regular graph. Part A: Let G (X,Y,E) be a regular bipartite graph, prove that |X| = |Y]. Part B: Use Hall's theorem to prove that, if G = (X,Y, E) is a regular bipartite graph, then there is a matching of size |X|. Part C: Let G = (X,Y,E) be a k-regular bipartite graph, then the edge set of G can be partitioned into k matchinga which do not share any common edge. (Hint: you may want to use induction.)