On unavoidability of trees with \(k\) leaves (Q1396655)

Let \(g(k)\) denote the least integer such that every oriented tree with \(n\) vertices and \(k\) leaves is contained in every tournament with \(n+g(k)\) vertices. The author and S. Thomassé have conjectured that \(g(k) \leq k-1\); see [Discrete Math. 243, 121-134 (2002; Zbl 0995.05037)]. In the present paper the author proves this conjecture for a certain restricted family of oriented trees that he calls constructible.