(a) (b) (C) Show that a connected graph with at least as many edges as vertices must contain a cycle. Let G be a connected graph with n vertices and m edges for n 2 2. Show that G contains a bipartite subgraph H := H (V, E) with the same vertex set as G (i.e V(H) = V(G)) and |E(H)l 2 %. you should be able to give a construction of this graph, proving why it has at least % edges. Let K be a connected graph with n vertices and at least 271 1 edges for n 2 2. Show that K must contain a cycle of even length