A result on Hamiltonian cycles in generalized Petersen graphs

Abstract

The generalized Petersen graph G(n, k) , 1≤ k ≤ n −1, is defined as follows: The graph G(n, k) has vertices v 0 , v 1 , …, v n−1 , v′ 0 , v′ 1 , …, v′ n−1 and edges v i v i+1 , v′ i v′ i+k and v i v′ i for all i with 0≤ i ≤ n −1 with all subscripts taken modulo n . In this paper we show that for each k >2 there exists an n(k) such that whenever n≥n(k) , then G(n, k) has a Hamiltonian cycle.