1. Prove, disprove (give a counterexample, highlight the incorrectness or give the correct answer) or complete a proof. (i) G is a 2-connected graph, and let C be any cycle in G. Consider the collection H of all subgraphs of G that are Whitney synthesis from cycle C. Since the collection H is nonempty (C H), there exists a subgraph * e H with the maximum number of edges and H*#G. Then, the connectedness of G implies that there exists an edge e = vwe Eg-Eir whose endpoint v lies in H and w does not lies in H*. Furthermore, we can find a cycle passing v and containing w, all vertices of which except v are not in H