New sufficient condition and Hamiltonian and traceable
Kewen Zhao, Li Zu, Deqin Chen · Journal of Discrete Mathematical Sciences and Cryptography · 2011
In 1952 Dirac introduced degree type condition and proved if G is a connected graph of order n ≥ 3 such that δ (G) ≥ n/2, then G is Hamiltonian. In this paper we prove further result that if G is a connected graph of order n ≥ 3 such that δ (G) ≥ (n – 2)/2, then G is Hamiltonian or G belongs to four classes of exceptional graphs, and then G is traceable or G belongs to a classes of exceptional graphs