Ringi Kim (김린기), Unavoidable subtournaments in tournaments with large chromatic number

For a tournament T, the chromatic number of T is the minimum number of transitive sets with union V(T). We say a set ? of tournaments is heroic if there exists c such that every tournament excluding all members of ? has chromatic number at most c. Berger et al. explicitly characterized all heroic sets of size one. In this talk, we study heroic sets of size two. This is a joint work with Maria Chudnovsky, Ilhee Kim, and Paul Seymour.