Busch, Arthur H. A note on the number of Hamiltonian paths in strong tournaments. (English) Zbl 1080.05038 Electron. J. Comb. 13, No. 1, Research paper N3, 4 p. (2006). 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. Cited in 5 Documents MSC: 05C20 Directed graphs (digraphs), tournaments 05C38 Paths and cycles 05C45 Eulerian and Hamiltonian graphs PDFBibTeX XMLCite \textit{A. H. Busch}, Electron. J. Comb. 13, No. 1, Research paper N3, 4 p. (2006; Zbl 1080.05038) Full Text: EuDML EMIS Online Encyclopedia of Integer Sequences: Smallest label f(T) given to a rooted tree T with n nodes in Matula-Goebel labeling.