无爪图周长的一个下界

A Below Bound on Circumferences of Claw-free Graph

本文主要证明了下面两个结论：（一）设Ｇ是３－连通无爪图，若存在顶点ｘ∈ｖ（Ｇ）使，则Ｇ是Ｈ－图。（二）设Ｃ是ｎ阶尽连通无爪图（ｋ≥２），则ｃ的周长ｃ（Ｇ）≥。

In this paper the author mainly proved the following two results:(1)Let G be a 3-con-nected K1.3-free graph,if there is a vertex x∈V(G)that satisfies max d(x,y)≤2,then G is 8H-graph.(2)Let G be a k-connected K1.3-free graph order n(k≥2),then(G)≥min{n,2δ+2+2[k/2](d-3)}.