A digraph is n-unavoidable if it is contained in every tournament of order n. We first prove that every arborescence of order n with k leaves is $(n+k-1)$-unavoidable. We then prove that every oriented tree of order n ($n\ge 2$) with k leaves is $(\frac{3}{2}n+\frac{3}{2}k-2)$-unavoidable and $(\frac{9}{2}n-\frac{5}{2}k-\frac{9}{2})$-unavoidable, and thus $(\frac{21}{8}n-\frac{47}{16})$-unavoidable. Finally, we prove that every oriented tree of order n with k leaves is $(n+144k^2-280k+124)$-unavoidable.

中文翻译：

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关于定向树的不可避免性

一个有向图是n-不可避免的，如果它包含在n阶的每个锦标赛中。我们首先证明每个具有k 个叶子的n阶树状结构是$(n+克-1)$——不可避免。然后我们证明每个n阶有向树($n\ge 2$) 有k 个叶子是$(\frac{3}{2}n+\frac{3}{2}克-2)$-不可避免和 $(\frac{9}{2}n-\frac{5}{2}克-\frac{9}{2})$-不可避免，因此 $(\frac{21}{8}n-\frac{47}{16})$——不可避免。最后，我们证明每棵有k 个叶子的n阶有向树是$(n+144{克}^2-280克+124)$——不可避免。