We show that any graph that is generically globally rigid in ℝ d has a realization in ℝ d that is both generic and universally rigid. This also implies that the graph also must have a realization in ℝ d 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.

中文翻译：

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通用的全局刚性图具有通用的通用刚性框架

我们表明，任何在 ℝ d 中通用全局刚性的图在 ℝ d 中都有一个实现，它既是通用的又是普遍刚性的。这也意味着该图也必须在ℝ d 中具有无限小刚性和普遍刚性的实现；这种认识可作为通用全球刚性的证明。我们的方法涉及 Lovász、Saks 和 Schrijver 的算法，该算法为充分连接的图构建顶点的一般位置正交表示，以及 Alfakih 的结果，该结果显示了这种表示如何导致应力矩阵和普遍刚性框架图。