Toughness for the existence of k-Hamiltonian [a, b]-factors

被引:0
|
作者
Zhou, Sizhong [1 ]
Xu, Yang [2 ]
Yang, Fan [1 ]
机构
[1] Jiangsu Univ Sci & Technol, Sch Math & Phys, Mengxi Rd 2, Zhanjiang 212003, Jiangsu, Peoples R China
[2] Qingdao Agr Univ, Dept Math, Qingdao 266109, Shandong, Peoples R China
基金
中国国家自然科学基金;
关键词
toughness; k-Hamiltonian graph; k-Hamiltonian; a; b]-factor; GRAPHS; CYCLE;
D O I
暂无
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let a, b and k be three nonnegative integers with a >= 2 and b >= a(k + 1) + 2. A graph G is called a k-Hamiltonian graph if G - U contains a Hamiltonian cycle for every subset U subset of V (G) with vertical bar U vertical bar = k. An [a, b]-factor F of G is called a Hamiltonian [a, b] factor if F contains a Hamiltonian cycle. If G - U has a Hamiltonian [a, b]-factor for every subset U subset of V(G) with vertical bar U vertical bar = k, then we say that G admits a k-Hamiltonian [a, b] -factor. Suppose that G is a k Hamiltonian graph of order n with n >= a + k + 2. In this paper, it is proved that G includes a k-Hamiltonian [a, b]-factor if delta(G) >= a + k and t(G) >= a - 1 + (a - 1)(k + 1)/b - 2.
引用
收藏
页码:153 / 161
页数:9
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