Let a, b, k be nonnegative integers with 2 ≤ a < 6. A graph G is called a k-Hamiltonian graph if G − U contains a Hamiltonian cycle for any subset U ⊆ V(G) with ∣U∣ = k. An [a, b]-factor F of G is called a Hamiltonian [a, b]-factor if F contains a Hamiltonian cycle. If G − U admits a Hamiltonian [a, b]-factor for any subset U ⊆ V(G) with ∣U∣ = k, then we say that G has a k-Hamiltonian [a, b]-factor. Suppose that G is a k-Hamiltonian graph of order n with \(n\geq\frac{(a+b-4)(2a+b+k-6)}{b-2}+k\) and δ(G) ≥ a + k. In this paper, it is proved that G admits a k-Hamiltonian [a, b]-factor if \(\max\{d_{G}(x),d_{G}(y)\}\geq\frac{(a-2)n+(b-2)k}{a+b-4}+2\) for each pair of nonadjacent vertices x and y in G.

让A，B，K与非负整数2≤一个<6.一种图形ģ称为ķ -Hamiltonian图表如果ģ - U包含任何子集的哈密顿周期ù ⊆ V（G ^用）| Ù | = ķ。如果F包含哈密顿循环，则G的[ a，b ]因子F称为哈密顿[ a，b ]因子。如果G ^ - U录取哈密顿[ A，B ] -因子对于任意子集Ü ⊆ V（G ^），其中∣ U ∣ = k，那么我们说G具有k -Hamiltonian [ a，b ]因子。假设ģ是ķ的顺序-Hamiltonian图表Ñ与\（N \ GEQ \压裂{（A + B-4）（2A + B + K-6）} {B-2} + K \）和δ（ģ）≥一个+ ķ。在本文中，证明了ģ承认一个ķ -Hamiltonian [ A，B ] -因子如果\（\最大\ {D_ {G}（x）时，D_ {G}（Y）\} \ GEQ \压裂{每对不相邻的顶点x和（a-2）n +（b-2）k} {a + b-4} +2 \）y在G中。