Consider a graph G such that at least one vertex v is connected to all other vertices. Prove that G is not bipartite.
That's the question, however, I don't think it can be proven. I think there's something wrong with the question but I'm not sure.
what if you had a graph with three vertices A,B,C and there were edges A-B and A-C. Vertex A would be connected to all other vertices and yet the graph is still bipartite based on the two color theorem.
Am I missing something here?