Bipartite proof Let $G$ be a graph of order $5$ or more. Prove that at most one of $G$ and "$G$ complement" is bipartite. 
I'm lost as to what needs to be done. I know that A nontrivial graph $G$ is bipartite if and only if $G$ contains no odd cycles.

What is needed here is Ramsey's theorem.
http://en.wikipedia.org/wiki/Ramsey_theorem
In particular, Ramsey's theorem says that every Graph with 6 or more vertices either has a clique of size three, or its complement has a clique of size three.
