Powers of Directed Hamiltonian Paths as Feedback Arc Sets

Given an acyclic digraph \( D \), we seek a smallest sized tournament \( T \) having \( D \) as a minimum feedback arc set. The reversing number of a digraph is defined to be

\[
r(D) = |V(T)| – |V(D)|.
\]

We use integer programming methods to obtain new results for the reversing number where \( D \) is a power of a directed Hamiltonian path. As a result, we establish that known reversing numbers for certain classes of tournaments actually suffice for a larger class of digraphs.