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.
Department, Program, or Center
School of Mathematical Sciences (COS)
J. Baldwin, W. Kronholm, and D. Narayan. Tournaments with a transitive subtournament as a feedback arc set. Congressus Numerantium 158 (2002), 51-58.
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