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 3 . 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. A tournament T = (V, A) is an oriented complete graph. Let hp(T) be the number of distinct hamiltonian paths in T (i.e., directed paths that include every vertex of V ). It is well known that hP (T) = 1 if and only if T is transitive, and R

• Type: Journal
• Year: 2006
• Where: COMBINATORICS
• Authors: Arthur H. Busch
• Keywords: COMBINATORICS 2006, Distinct Hamiltonian Paths, Minimum Number, Strong Tournament