Let A and B be 2 Eulerian graphs with no common vertices. Let v1 be a vertex of A and v2 be a vertex of B. Let G be the graph that is formed by taking AUB and adding the edge v1v2. What can be said about G?
Is it simply that G is Eulerian since we are just adding one more edge and we are not changing the number of vertices, or is there something else that can be said?