On tournaments and their largest transitive subtournaments (Q1343231)

For each positive integer \(n\), let \(v(n)\) denote the largest integer such that every tournament of order \(n\) contains a transitive subtournament of order \(v(n)\). The author presents a quick survey of what is known about \(v(n)\). He then proves that there is a unique tournament of order 27 not containing a transitive tournament of order 6. He then goes on to show that every tournament of order 55 contains a transitive tournament of order 7.