Let n be the number of vertices of G. Recall that G denotes the complement of G. Show that a) n ≤ χ(G)χ(G) and therefore, b) χ(G) + χ(G) ≥ 2√n.

This question was on my graph theory exam and I didn’t know how to approach solving it. The question in Tex is as follows:

Let n be the number of vertices of G. Recall that G denotes the complement of G. Show that a) n ≤ χ(G)χ(G) and therefore, b) χ(G) + χ(G) ≥ 2√n.

Any tips on how to approach this would be greatly appreciated!