On local characterizations of Hamiltonian tournaments (Q1313195)

The authors prove that a strong tournament \(T_ n\) \((n \geq 6)\) has just one spanning cycle if and only if each of its strong subtournaments \(T_ 6\) has just one spanning cycle; and a strong tournament \(T_ n\) \((n \geq 5)\) has only \((n-2)\) 3-cycles if and only if each of its strong subtournaments \(T_ 5\) has only three 3-cycles.