Grinberg's Criterion Applied to Some Non-Planar Graphs
Gek Ling Chia, Carsten Thomassen · Technical University of Denmark, DTU Orbit (Technical University of Denmark, DTU) · 2011
Robertson ([5]) and independently, Bondy ([1]) proved that the generalized Petersen graph P (n, 2) is non-hamiltonian if n ≡ 5 ( mod 6), while Thomason [7] 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 [6].In this note we give a short unified proof of these results using Grinberg's theorem.