On Tournaments with Domination Number Exactly \(k\)

Jack R. Duncan 1, Michael S. Jacobson 1
1University of Louisville Louisville, KY 40292, U.S.A.

Abstract

In this paper, we establish that for arbitrary positive integers k and m, where \(k > 1\), there exists a tournament which has exactly m minimum dominating sets of order k. A construction of such tournaments will be given.