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.

Publication Date



The authors thank Garth Isaak and Stanislaw Radziszowski for valuable discussions and input.

Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works in February 2014.

Document Type


Department, Program, or Center

School of Mathematical Sciences (COS)


RIT – Main Campus