Let a and b be nonnegative integers with 2 ≤ a < b, and

\r\nlet G be a Hamiltonian graph of order n with n ≥ (a+b−4)(a+b−2)

\r\nb−2 .

\r\nAn [a, b]-factor F of G is called a Hamiltonian [a, b]-factor if F

\r\ncontains a Hamiltonian cycle. In this paper, it is proved that G has a

\r\nHamiltonian [a, b]-factor if |NG(X)| > (a−1)n+|X|−1

\r\na+b−3 for every nonempty

\r\nindependent subset X of V (G) and δ(G) > (a−1)n+a+b−4

\r\na+b−3 .<\/p>\r\n","references":null,"publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 33, 2009"}