(a) Let G = (V, E) be a connected bipartite undirected graph with V partitioned as V1 ∪ V2. Prove that if |V1| + |V2|, then G cannot have a Hamilton cycle.
(b) Prove that if the graph G in part (a) has a Hamilton path, then |V1| - |V2| = ± 1.
(c) Give an example of a connected bipartite undirected graph G = (V, E), where V is partitioned as V1 ∪ V2 and |V| = |V2| - 1, but G has no Hamilton path.