Hamiltonian degree conditions for tough graphs Original Research Article

We prove the following theorem: Let G be a graph with degree sequence d1, d2,…,dn and let t be a positive integer at most three. If G is t-tough and ∀i, t ⩽ i < n/2, di ⩽ i ⇒ dn-i+t ⩾ n - i then G is hamiltonian. In the case t = 1, our theorem generalizes a well-known theorem of Chvátal. A similar result is established for pancyclic graphs.