Hamiltonian cycles in 1-tough graphs

For a graphG, let₃ = min{_i=1³ d(u_i): {u₁, u₂, u₃} is an independent set ofG} and = min{_i=1³ d(u_i) – is an independent set ofG}. In this paper, we shall prove the following result: LetG be a 1-tough graph withn vertices such that₃ n and – 4. ThenG is hamiltonian. This generalizes a result of Fassbender [2], a result of Flandrin, Jung and Li [3] and a result of Jung [5].Supported in part by das promotionsstipendium nach dem NaFöG and the Post-Doctoral Foundation of China.