We show that for every positive integer k, any tournament with minimum out-degree at least $(2+o(1))k^2$ contains a subdivision of the complete directed graph on k vertices, where each path of the subdivision has length at most 3. This result is best possible on the minimum out-degree condition (up to a multiplicative factor of 8), and it is tight with respect to the length of the paths. It may be viewed as a directed analogue of a theorem proved by Bollobás and Thomason, and independently by Komlós and Szemerédi, concerning subdivisions of cliques in graphs with sufficiently high average degree. We also consider the following problem: given k, what is the smallest positive integer $f(k)$ such that any $f(k)$-vertex tournament contains a 1-subdivision of the transitive tournament on k vertices? We show that $f(k)=O(k^2{\log }^{3}k)$ which is best possible up to the logarithmic factors.

我们显示出，对于每个正整数k，任何具有最小出学位的比赛至少$（2+Ø（\mathrm{1个}））{ķ}^2$包含一个完整的有向图在k个顶点上的细分，该细分的每个路径的长度最大为3。在最小向外度条件下（乘数最大为8），此结果是最好的，并且它很紧关于路径的长度。可以将其视为由Bollobás和Thomason证明的定理的有向类似物，并且可以由Komlós和Szemerédi独立地证明，该定理涉及具有足够高平均度的图中的集团细分。我们还考虑以下问题：给定k，最小正整数是多少$F（ķ）$ 这样任何 $F（ķ）$-vertex竞赛在k个顶点上包含传递竞赛的1细分？我们证明$F（ķ）=Ø（{ķ}^2{\mathrm{日志}}^3ķ）$ 根据对数因子，这是最可能的。