| Abstract: | An oriented tree T on n vertices is unavoidable if every tournament on n vertices contains a copy of T. In this paper, we give a sufficient condition for T to be unavoidable, and use this to prove that almost all labeled oriented trees are unavoidable, verifying a conjecture of Bender and Wormald. We additionally prove that every tournament on  vertices contains a copy of every oriented tree T on n vertices with polylogarithmic maximum degree, improving a result of Kühn, Mycroft, and Osthus. |
