A cutset in a connected graph G is a set K of edges whose removal disconnects G, but the removal of any proper subset of K does not disconnect G. For example, in the graph in problem 7, the set K ={(a, f), (b, g), (C,h), (d,i), (e,j)} is a cutset separating {a,b,c,d,c} from the rest of the vertices, while no proper subset of these 5 edges disconnects the graph. Find a cutset in the right graph in problem 1 with 4 edges. Explain briefly why any spanning tree of a connected graph G must intersect any cutset of G. If K is a cutset in a connect graph G and C is a circuit in G, explain briefly why K and C must have an even number of edges in common (possibly zero). Give a careful argument to show that this graph has no Hamilton circuit