  For a set H of tournaments, we say H is heroic if every tournament, not
containing any member of H as a subtournament, has bounded chromatic number.
Berger et al. explicitly characterized all heroic sets containing one
tournament. Motivated by this result, we study heroic sets containing two
tournaments. We give a necessary condition for a set containing two tournaments
to be heroic. We also construct infinitely many minimal heroic sets of size
two.
