Maximal number of leaders in the tournament. > Let's call a leader in the tournament such participant $L$, that won with every other participant directly or indirectly. Show that a leader always exists. Find the maximal number of leaders in the tournament with $n$ participant. So far, I was able to prove that a leader in the tournament always exists (considering spanning road (such road that visit every vertex once). But I have no idea how to prove the second part: maximal number of leaders. Any HINTS how to start with the second part?

HINT: What if the tournament includes a large directed cycle?