论文标题
在全球刚性图上的猜想的最小反例
Minimal counterexamples to Hendrickson's conjecture on globally rigid graphs
论文作者
论文摘要
在本文中，我们考虑了$ d $ rigid和$（d+1）$ - 连接但不是全球$ d $ rigid的图表类别，其中$ d $是尺寸。该课程来自布鲁斯·亨德里克森（Bruce Hendrickson）的反例到猜想。对于给定数量的顶点，该类中的图形相对较少。使用计算，我们表明$ k_ {5,5} $确实是猜想的最小反例。
In this paper we consider the class of graphs which are redundantly $d$-rigid and $(d+1)$-connected but not globally $d$-rigid, where $d$ is the dimension. This class arises from counterexamples to a conjecture by Bruce Hendrickson. It seems that there are relatively few graphs in this class for a given number of vertices. Using computations we show that $K_{5,5}$ is indeed the smallest counterexample to the conjecture.
