No minimal imperfect graph of order 200 Prove that there is no minimal imperfect graph of order 200, without using the Strong Perfect Graph Theorem.

It is well-known that for a p-critical graph $|G|=\alpha(G)\omega(G)+1$ (where $\alpha$ is the independence number and $\omega$ the clique number) and that they have both $\alpha(G)$ and $\omega(G)$ at least 2. Since 199 is prime this is a contradiction. Do you need proofs of any of the statements (they are not very hard)?