Largest digraphs contained in all n-tournaments (Q788740)

Let f(n) denote the largest integer such that there exists a directed graph D with n vertices and f(n) edges that is contained in every tournament with n vertices. The authors show, among other things, that \(c_ 1n\leq n \log_ 2n-f(n)\leq c_ 2n \log \log n\) for suitable constants \(c_ 1\) and \(c_ 2\).