  The celebrated Erd\"{o}s-Hajnal conjecture states that for every undirected
graph $H$ there exists $ \epsilon(H) > 0 $ such that every undirected graph on
$ n $ vertices that does not contain $H$ as an induced subgraph contains a
clique or a stable set of size at least $ n^{\epsilon(H)} $. This conjecture
has a directed equivalent version stating that for every tournament $H$ there
exists $ \epsilon(H) > 0 $ such that every $H$-free $n$-vertex tournament $T$
contains a transitive subtournament of order at least $ n^{\epsilon(H)} $. This
conjecture is proved for few infinite families of tournaments. In this paper we
construct a new infinite family of tournaments $-$ the family of so-called
flotilla-galaxies and we prove the correctness of the conjecture for every
flotilla-galaxy tournament.
