A result on Hamiltonian cycles in generalized Petersen graphs

The generalized Petersen graph G(n, k), 1≤k≤n−1, is defined as follows: The graph G(n, k) has vertices v0, v1, …, vn−1, v′0, v′1, …, v′n−1 and edges vivi+1, v′iv′i+k and viv′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