Question: Let G be a graph that contains an Eulerian circuit and let V(G) = AUB be a disjoint union of its vertices. Prove that the

Let G be a graph that contains an Eulerian circuit and let V(G) = AUB be a disjoint union of its vertices. Prove that the number of edges with one end in A and the other end in B is even (note that G is not necessarily bipartite: there can be edges between the elements in A and edges between the elements of B)

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