Grinberg's criterion applied to some non-planar graphs - Chia, G.L.; Thomassen, C. (2010)
Robertson ([3]) and independently, Bondy ([1]) proved that the generalized Petersen graph P(n,2) is non-hamiltonian if n == 5 (mod 6), while Thomason ([5]) proved that it has precisely 3 hamiltonian cycles if n == 3 (mod 6). The hamiltonian cycles in the remaining generalized Petersen graphs were enumerated by Schwenk ([4]). In this note we give a short unified proof of these results using Grinberg's theorem.