Answer: 4k-1 Construction for 4k-2: take two tournaments of size 2k-1 where each vertex has out-degree k-1, and then connect them with a fixed orientation. Upper bound: partition the vertices into 2 groups: A - where the vertices have a bigger in-degree and B - where the vertices have bigger out-degree. WLOG A has at least 2k vertices, then by looking at these 2k vertices as a separate tournament, it’s clear that at least 1 vertex has out degree bigger than or equal to k. Done