论文标题
锦标赛中的道路力量的注释
A Note on Powers of Paths in Tournaments
论文作者
论文摘要
在本说明中，我们表明，$ n $ Vertices上的每场比赛都包含$ k $ - $ k $ the的电源，其长度为$ n/2^{6k+7} $，它在Scott和Scott和Korándi的最新界限上有所改善，为$ N/2^{2^{2^{3K}}} $。通过这样做，我们获得了对$ k $的反指数依赖，这是Yuster最近显示的$ kN/{2^{k/2}} $的上限。
In this note we show that every tournament on $n$ vertices contains the $k$-th power of a directed path of length $n/2^{6k+7}$, which improves upon the recent bound of Scott and Korándi of $n/2^{2^{3k}}$. By doing so, we get an inverse exponential dependence on $k$, which is best possible as Yuster recently showed an upper bound of $kn/{2^{k/2}}$.
