  We study combinatorial and algorithmic questions around minimal feedback
vertex sets in tournament graphs.
  On the combinatorial side, we derive strong upper and lower bounds on the
maximum number of minimal feedback vertex sets in an n-vertex tournament. We
prove that every tournament on n vertices has at most 1.6740^n minimal feedback
vertex sets, and that there is an infinite family of tournaments, all having at
least 1.5448^n minimal feedback vertex sets. This improves and extends the
bounds of Moon (1971).
  On the algorithmic side, we design the first polynomial space algorithm that
enumerates the minimal feedback vertex sets of a tournament with polynomial
delay. The combination of our results yields the fastest known algorithm for
finding a minimum size feedback vertex set in a tournament.
