1.Let G be a simple graph with (G) 3. 2.Show that if G is a simple graph with Prove that (G) |V(G) | 2 k'(G) k(G) then k(G) (G) 3. Let G be a 2-connected graph so and e an edge in G. Prove that G - e is 2connected if and only if the endpoints of e lie in a cycle in G - e. 4. Let 1 and 2 be distinct colors of a k- coloring of G. Call an edge e a 12 edge if the colors on the end points of e are 1 and 2. Thus e has coloration 12. If |E (G)| > . k ( ) 2 Show that at least 2 edges of G have the same type of coloration