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A note on the number of Hamiltonian paths in strong tournaments. (English) Zbl 1080.05038

Summary: We prove that the minimum number of distinct Hamiltonian paths in a strong tournament of order \(n\) is \(5^{\frac {n-1}3}\). A known construction shows this number is best possible when \(n \equiv 1 \bmod 3\) and gives similar minimal values for \(n\) congruent to 0 and 2 modulo 3.

MSC:

05C20 Directed graphs (digraphs), tournaments
05C38 Paths and cycles
05C45 Eulerian and Hamiltonian graphs
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