On Sets of Arcs Containing No Cycles in a Tournament*
K. B. Reid · Canadian Mathematical Bulletin · 1969
A tournament Tn with n nodes is a complete asymmetric digraph [2]. A set S of arcs of a tournament is called consistent if the tournament contains no oriented cycles composed entirely of arcs of S [1]. The object of this note is to provide a new lower bound for f(n), the greatest integer k such that every tournament with n nodes contains a set of k consistent arcs. Erdös and Moon [1] showed that where [x] denotes the largest integer not exceeding x, and the second inequality holds for any fixed ∈ > 0 and all sufficiently large n.