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.

Assume one of them is bipartite. So, at least one of parts has 3 or more vertices. Let's pick 3 of them and call them u, v, w. As these 3 vertices are in the same part, they have no connection.  Therefore, in the complement graph there are uv, uw and vw edges. Now, u, v, w, u is a cycle of length 3 and it shows that complement graph could not be bipartite. 
