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.
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)