Question 3 (Degrees and Cycles, 30 points) Recall that for a graph G that the degree of a vertex v is the number of edges with v as an endpoint. Recall that a cycle is a sequence of vertices vi, U2,... , Un so that there are edges vi to v2, v2 to v3,. .. , Vn-1 to vn and from vn to vi, where additionally no edge is used more than once in this sequence (a) Show that for any finite graph G where all vertices of G have degree at least 2 that G contains a cycle. Hint: Start at some verter v of G and follow edges until a vertez is reached for the second time.) [10 points (b) Is it the case that every vertez of v is necessarily contained in a cycle? Prove that this is the case or provide a counter-erample. [10 points (c) Suppose instead that every vertex of G has degree exactly equal to 2. Is it the case that every vertex of G is contained in a cycle? 10 points