Will a strong tournament still be a strong tounament after removing a vertex from it?

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I was trying to prove a theorem in a new way other than the one our doctor gave us, but there is a step that I am not sure of.

If $G$ is a strong tournament is there a vertex that can be removed from the graph for the graph to still be a strong tournament?

I think its not true for ANY vertex, but can we find 1? Or more than 1? And is there a condition for that?