Sumner's universal tournament conjecture states that every (2n−2)-vertex tournament should contain a copy of every n-vertex oriented tree. If we know the number of leaves of an oriented tree, or its maximum degree, can we guarantee a copy of the tree with fewer vertices in the tournament? Due to work initiated by Häggkvist and Thomason (for number of leaves) and Kühn, Mycroft and Osthus (for maximum degree), it is known that improvements can be made over Sumner's conjecture in some cases, and indeed sometimes an (n+o(n))-vertex tournament may be sufficient.

中文翻译：

---

锦标赛中有很多叶子的树


Sumner 的通用锦标赛猜想指出，每个 （2n−2） 顶点锦标赛都应该包含每个面向 n 顶点的树的副本。如果我们知道一棵定向树的叶子数，或者它的最大度数，我们能否保证在比赛中该树的顶点数量较少？由于 Häggkvist 和 Thomason（关于叶子的数量）以及 Kühn、Mycroft 和 Osthus（关于最大程度）发起的工作，众所周知，在某些情况下可以对 Sumner 的猜想进行改进，事实上，有时 （n+o（n）） 顶点锦标赛可能就足够了。