A digraph isn-unavoidableif it is contained in every tournament of ordern. We first prove that every arborescence of ordernwithkleaves is (n+k ?1)-unavoidable. We then prove that every oriented tree of ordernwithkleaves is(32n+32k?2)-unavoidable and(92n?52k?92)-unavoidable, and thus(218(n?1))-unavoidable. Finally, we prove that every oriented tree of ordernwithkleaves is (n+144k2?280k+124)-unavoidable.
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