A Note on the Number of Hamiltonian Paths in Strong Tournaments - Busch, Arthur H. (The Electronic Journal of Combinatorics, 2006)
We prove that the minimum number of distinct hamiltonian paths in a strong tournament of order n is 5^n-13 . A known construction shows this number is best possible when n 1 mod 3 and gives similar minimal values for n congruent to 0 and 2 modulo 3.