Would love some help on this graph theory question. Thank you!

For a graph G, define x(G) to be the smallest value of k for which it is possible to assign one of k colours to each vertex such that no two adjacent vertices are assigned the same colour. For example, x(C6) = 2 and x(K6) = 6. (a) Prove that x(G) 2. (c) Prove that if G is a graph on 6 vertices with 13 edges, then x(G) > 3