Generically Globally Rigid Graphs Have Generic Universally Rigid Frameworks
Generically Globally Rigid Graphs Have Generic Universally Rigid Frameworks
复制标题
通用全局刚性图具有通用通用刚性框架
作者：
R. Connelly;S. Gortler;Louis Theran
我们表明，任何图，是一般的全球刚性的，在BHD有一个实现BHD是通用的和普遍刚性的。这也意味着，图也必须有一个实现，即无限小刚性和普遍刚性;这样的实现作为一般全局刚性的证明。我们的方法涉及到一个算法由Lovász，Saks和Schrijver，对于一个充分连接的图，构造一个一般的位置正交表示的顶点，和结果的Alfakih，显示了这种表示如何导致一个应力矩阵和一个普遍刚性框架的图。
We show that any graph that is generically globally rigid in ℝd has a realization in ℝd that is both generic and universally rigid. This also implies that the graph also must have a realization in ℝd that is both infinitesimally rigid and universally rigid; such a realization serves as a certificate of generic global rigidity. Our approach involves an algorithm by Lovász, Saks and Schrijver that, for a sufficiently connected graph, constructs a general position orthogonal representation of the vertices, and a result of Alfakih that shows how this representation leads to a stress matrix and a universally rigid framework of the graph.
DOI：
10.1016/j.aam.2015.09.009
发表时间：
2015-10
期刊：
Adv. Appl. Math.
影响因子：
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作者：
J. Herzog;Antonio Macchia;S. Madani;V. Welker
通讯作者：
J. Herzog;Antonio Macchia;S. Madani;V. Welker