Problem: Let $k$ be a positive integer, and let $G$ be a bipartite graph in which every vertex has degree $k.$ Prove that the edges of $G$ can be partitioned into $k$ perfect matchings.
My Attempt: By simple application of Hall's Theorem, I have shown that $G$ has a perfect matching. However, I am not sure that I understand the language of the problem, i.e. what do we have to prove? What do you mean by the sentence that " the edges can be partitioned into $k$ perfect matchings". This does not make sense to me and I am unable to trace a related definition in my textbook. Please help!