Given a tournament with $2^n$ vertices, show that there is a sub-tournament with at least $n + 1$ vertices that is acyclic


So a tournament is just a complete directed graph, I believe.

I’m having trouble proving this problem. I know it is induction however. I was thinking the base case is $ 2^1$ vertices, and therefore we have a sub-tournament of 1 + 1 vertices, which holds.

Then in our induction step we have to show $ 2^{n + 1}$ . But I’m not sure how to approach this. Any ideas would be extremely appreciated.