Hello everyone!

I've found another interesting problem in graph theory and I would like your ideas.

Suppose that G is an infinite bipartite graph with vertex classes V1 and V2.

(a) Show that if V(G) is countable and every vertex has finite degree then Hall's condition implies the existence of a complete matching from V1 to V2.

(b)What happens if we drop the condition that every vertex has finite degree?