Tournaments with a Transitive Subtournament as a Feedback Arc Set

Given an acyclic digraph D, we seek a smallest sized tournament T that has D as a minimum feedback arc set. The reversing number of a digraph is defined to be r(D) = |V (T)|−|V (D)| . The case where D is a tournament Tn was studied by Isaak in 1995 using an integer linear programming formulation. In particular, this approach was used to produce lower bounds for r(Tn), and it was conjectured that the given bounds were tight. We examine the class of tournaments where n = 2k +2k−2 and show the known lower bounds for r(Tn) are best possible

A Classification of Tournaments Having an Acyclic Tournament as a Minimum Feedback Arc Set

Given a tournament with an acyclic tournament as a feedback arc set we give necessary and sufficient conditions for this feedback arc set to have minimum size