Subdivisions of digraphs in tournaments

We show that for every positive integer k, any tournament with minimum out-degree at least (2+o(1))k2 contains a subdivision of the complete directed graph on k vertices, where each path has length most 3. This result is best possible condition (up to multiplicative factor 8), and it tight respect paths. It may be viewed as analogue theorem proved by Bollobás Thomason, independently Komlós Szemerédi, concerning subdivisions cliques in graphs sufficiently high average degree. also consider following problem: given what smallest f(k) such f(k)-vertex 1-subdivision transitive vertices? f(k)=O(k2log3?k) which up logarithmic factors.