On the maximum cardinality of a consistent set of arcs in a random tournament (Q788001)

Let \(f(T_ n)\) denote the maximum number of arcs possible in an acyclic subgraph of a random tournament \(T_ n\). The author shows that \(f(T_ n)<n(n-1)/4+1.73n^{3/2}\) with probability tending to one as n tends to infinity, thereby sharpening a result of \textit{J. Spencer} [Period. Math. Hung. 11, 131-144 (1980; Zbl 0349.05011)].