Hamiltonian cycles in generalized petersen graphs

Watkins (J. Combinatorial Theory 6 (1969), 152–164) introduced the concept of generalized Petersen graphs and conjectured that all but the original Petersen graph have a Tait coloring. Castagna and Prins (Pacific J. Math. 40 (1972), 53–58) showed that the conjecture was true and conjectured that generalized Petersen graphs G(n, k) are Hamiltonian unless isomorphic to G(n, 2) where n ≡ 5(mod 6). The purpose of this paper is to prove the conjecture of Castagna and Prins in the case of coprime numbers n and k.