3连通3正则权图圈权的一个猜想的证明

本文证实了Ｂｏｎｄｙ的猜想．证明了：设 Ｇ为简单 ３连通 ３正则权图，｜Ｖ（Ｇ）｜＝ｎ＞６，则Ｇ含圈Ｃ，使Ｗ（Ｃ）＞４Ｗ（Ｇ）／ｎ．

Proof of Conjecture about the Weight of Cycle in 3-Connected 3-Regular Weighted Graph

Bondy proposed a conjecture as follows: Let G be a simple 2-connected 3-regu- lar weighted graph on n vertices where n>6. Then G would contain a cycle of weight at least 4W(G)/ n. If the connectivity of G equals to two, the conjecture would be true. This paper further proves that if the connectivity of G equals to three, the conjecture is also true.