关于赋权图中重圈的一个范型定理

设G=(V, E; w)为赋权图,定义G中点v的权度d_G^w(v)为G中与v相关联的所有边的权和.该文证明了下述定理: 假设G为满足下列条件的2 -连通赋权图: (i) 对G中任何导出路xyz都有w(xy)=w(yz); (ii)对G中每一个与K_1,3或K_1,3+e同构的导出子图T, T中所有边的权都相等并且min{max{d_G^w(x), d^w_G(y)}:d(x,y)=2,x,y∈ V(T)}≥ c/2. 那么, G中存在哈密尔顿圈或者存在权和至少为 c 的圈. 该结论分别推广了Fan^5], Bedrossian等人^2]和Zhang等人^7]的相关定理

A Fan Type Theorem for Heavy Cycles in Weighted Graphs

Let G=(V, E; w) be a weighted graph, and define the weighted degree d^w_G(v) of a vertex v in G as the sum of the weights of the edges incident with v. In this paper, the following theorem is proved: suppose G is a 2-connected weighted graph, where (i) w(xy)=w(yz) for every induced path xyz, and (ii) in every induced subgraph T of G isomorphic to K_1,3 or K_1,3+e, all the edges of T have the same weight and min{max{d^w_G(x), d^w_G(y)} : d(x,y) =2,x,y ∈ V(T)}≥ c/2, then G contains either a Hamilton cycle or a cycle of weight c at least. This respectively generalizes three theorems of Fan^5], Bedrossian et al^2] and Zhang et al^7].