On complete strongly connected digraphs with the least number of 3-cycles

Abstract The least number of 3-cycles (cycles of length 3) that a hamiltonian tournament of order n can contain is n − 2 (see [3]). Since each complete strongly connected digraph contains a spanning hamiltonian subtournament (see [2]), n − 2 is also the least number of 3-cycles for these digraphs. In this paper we characterize the family of complete strongly connected digraphs with the least number of 3-cycles using the structural characterization of hamiltonian tournaments with the same extremal property (see [1]).