1 In each of the following cases, describe a suitable graph which has the properties stated, or prove that no such graph can exist. You may use any result from the lectures, provided that you state it clearly. Justify your answers. (a) There is a simple graph with 10 vertices and degree sequence (8,8,8,8,6,6,3,3,3,1). (b) There is a tree with 6 vertices, a vertex with degree 5, and a vertex with degree 2. (c) There is a simple graph with 10 vertices, 24 edges, and chromatic number 4. (d) There is a simple graph with 7 vertices, 10 edges, and no K3 as a subgraph. (e) There is a simple graph with 13 vertices, minimum degree 7, and no Hamilton cycle. (1) There is a simple bipartite graph with 7 vertices, 12 edges, and a Hamilton cycle.