Degree Conditions for k-Hamiltonian [a, b]-factors

• 作者: Jie WU Si-zhong ZHOU
• 来源期刊: 应用数学学报（英文版）
• 年，卷（期）: 2021,（2）
• 页码范围: 232-239
• 页数: 8页
• 语种: 英文

摘要

Let a,b,k be nonnegative integers with 2 ≤ a ＜ b.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 ≥ (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{dG(x),dG(y)} ≥ (a-2)n+(b-2)ka+b-4 + 2 for each pair of nonadjacent vertices x and y in G.