A Note on the Number of Hamiltonian Paths in Strong Tournaments
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 $3$.
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| Published in | The Electronic journal of combinatorics Vol. 13; no. 1 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
01.02.2006
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| Online Access | Get full text |
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| Summary: | 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 $3$. |
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| ISSN: | 1077-8926 1077-8926 |
| DOI: | 10.37236/1141 |