The study of problems concerning subdivisions of graphs has a rich history in extremal combinatorics. Confirming a conjecture of Burr and Erdős, Alon proved in 1994 that subdivided graphs have linear Ramsey numbers. Later, Alon, Krivelevich and Sudakov showed that every n-vertex graph with at least $\epsilon n^2$ edges contains a 1-subdivision of the complete graph on $c_{\epsilon }\sqrt{n}$ vertices, resolving another old conjecture of Erdős. In this paper we consider the directed analogue of these problems and show that every tournament on at least $(2+o(1))k^2$ vertices contains the 1-subdivision of a transitive tournament on k vertices. This is optimal up to a multiplicative factor of 4 and confirms a conjecture of Girão, Popielarz and Snyder.

关于图的细分问题的研究在极值组合学中有着丰富的历史。确认 Burr 和 Erdős 的猜想，Alon 在 1994 年证明了细分图具有线性 Ramsey 数。后来，Alon、Krivelevich 和 Sudakov 证明了每个n顶点图至少有$\epsilon n^2$边包含完整图的 1 细分$C_{\epsilon }\sqrt{n}$顶点，解决了 Erdős 的另一个古老猜想。在本文中，我们考虑这些问题的有向模拟，并表明每场比赛至少在$(2+○(1)){ķ}^2$vertices 包含k个顶点上的传递锦标赛的 1 细分。这是乘法因子 4 的最佳值，并证实了 Girão、Popielarz 和 Snyder 的猜想。