Formally prove the following: if depth first search finds a "back" edge, there is a cycle in the graph ,16 17,20 2,7 8,15 18,19 3 9,12 10,11 Tree edges: (a, s), (s, V), (v, w), (q, t), (t, x), (x, z), (t, y), (r, u) Back edges: (w, s), (z, x), (y, q) Forward edges: (q, W) Cross edges: (r, y), (u, y)