山东师范大学学报(自然科学版)

对 2 -连通非Hamilton赋权图G ,本文给出了重路存在的隐赋权度条件 :若G满足文中描述的条件C1 、C2 ,且max{idw(u) ,idw(v) |d(u ,v) =2 }≥ m2 ,则当G中存在y -最长路时 ,存在一最重的y-最长路P(x ,y)满足dw(x)≥ m2 .

In this paper we give an implicit weighted degree condition for heavy cycles in a 2-connected nonhamiltonian weighted gragh:suppose that G satisfies conditions C 1 and C 2 mentioned in the paper and max{id w(u),id w(v)|d(u,v)=2}≥m2.Then G contains a heaviest y-longest path P(x,y) such that d w(x)≥m2 if there exists a y- longest path in G.