## Chromatic number and graph complements

Let G be a graph with n vertices and let G' be its complement.

Prove that cr(G)*cr(G') >/= n.

I know that equality holds when G or G' are complete graphs.
From that, I know that switching an edge from the complete graph to the complement can decrease cr(G) by at most 1 but can double cr(G'). But it is too difficult to make an argument about switching edges in complicated graphs.