We prove that there exists $C>0$ such that any $(n+Ck)$-vertex tournament contains a copy of every n-vertex oriented tree with k leaves, improving the previously best known bound of $n+O(k^2)$ vertices to give a result tight up to the value of C. Furthermore, we show that, for each k, there exists $n_0$, such that, whenever $n⩾n_0$, any $(n+k-2)$-vertex tournament contains a copy of every n-vertex oriented tree with at most k leaves, confirming a conjecture of Dross and Havet.

中文翻译：

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比赛中叶子很少的树

我们证明存在$C>0$这样任何$(n+Cķ)$-vertex 锦标赛包含每个具有k个叶子的n- vertex 导向树的副本，改进了以前最知名的边界$n+○({ķ}^2)$顶点给出一个紧密到C值的结果。此外，我们证明，对于每个k，存在$n_0$, 这样, 每当$n⩾n_0$， 任何$(n+ķ-2)$-vertex 锦标赛包含每个n -vertex 导向树的副本，最多有k个叶子，证实了 Dross 和 Havet 的猜想。