A Generalization of Implicit Ore-condition for Hamiltonicity ofk-connected Graphs

被引：1
作者：
Cai, Jun-qing [1 ]
Wang, Lin [1 ]
机构：
[1] Qufu Normal Univ, Sch Management, Rizhao 276826, Peoples R China
来源：
ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES | 2020年 / 36卷 / 03期
基金：
中国国家自然科学基金;
关键词：
implicit degree; Hamiltonian cycle; cyclability; CYCLES;
D O I：
10.1007/s10255-020-0956-x
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In 2005, Flandrin et al. proved that ifGis ak-connected graph of ordernandV(G) =X-1?X-2? MIDLINE HORIZONTAL ELLIPSIS UXfc such thatd(x) +d(y) >= n for each pair of nonadjacent verticesx, y is an element of X(i)and eachiwithi= 1, 2, MIDLINE HORIZONTAL ELLIPSIS,k, thenGis hamiltonian. In order to get more sufficient conditions for hamiltonicity of graphs, Zhu, Li and Deng proposed the definitions of two kinds of implicit degree of a vertexv, denoted byid(1)(v) andid(2)(v), respectively. In this paper, we are going to prove that ifGis ak-connected graph of ordernandV(G) =X-1?X-2? MIDLINE HORIZONTAL ELLIPSIS ?X(k)such thatid(2)(x) +id(2)(y) >= nfor each pair of nonadjacent verticesx, y is an element of X(i)and eachiwithi= 1, 2, MIDLINE HORIZONTAL ELLIPSIS,k, thenGis hamiltonian.
引用
收藏
页码：620 / 626
页数：7
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