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

作　　者：Jun-qing CAI Lin WANG 

机构地区：[1]School of Management,Qufu Normal University,Rizhao 276826,China

出　　处：《Acta Mathematicae Applicatae Sinica》2020年第3期620-626,共7页应用数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China (No.11501322);Scientific Research Foundation for Doctors in Qufu Normal University (No. 2012015);Natural Science Foundation of Qufu Normal University (No.xkj201415)

摘　　要：In 2005,Flandrin et al.proved that if G is a k-connected graph of order n and V(G)=X1∪X2∪···∪Xk such that d(x)+d(y)≥n for each pair of nonadjacent vertices x,y∈Xi and each i with i=1,2,···,k,then G is 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 vertex v,denoted by id1(v)and id2(v),respectively.In this paper,we are going to prove that if G is a k-connected graph of order n and V(G)=X1∪X2∪···∪Xk such that id2(x)+id2(y)≥n for each pair of nonadjacent vertices x,y∈Xi and each i with i=1,2,···,k,then G is hamiltonian.

关 键 词：implicit degree Hamiltonian cycle CYCLABILITY 

分 类 号：O157.5[理学—数学]