Geodesic
A note on the number of Hamiltonian paths in strong tournaments
The electronic journal of combinatorics, Tome 13 (2006)
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We prove that the minimum number of distinct hamiltonian paths in a strong tournament of order $n$ is $5^{{n-1}\over{3}}$. A known construction shows this number is best possible when $n \equiv 1 \hbox{ mod } 3$ and gives similar minimal values for $n$ congruent to $0$ and $2$ modulo $3$.
DOI : 10.37236/1141
Classification : 05C20, 05C38, 05C45 
@article{10_37236_1141,
     author = {Arthur H. Busch},
     title = {A note on the number of {Hamiltonian} paths in strong tournaments},
     journal = {The electronic journal of combinatorics},
     year = {2006},
     volume = {13},
     doi = {10.37236/1141},
     zbl = {1080.05038},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1141/}
}
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Arthur H. Busch. A note on the number of Hamiltonian paths in strong tournaments. The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1141

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