SIAM Journal on Discrete Mathematics, Volume 35, Issue 1, Page 325-361, January 2021.
We interpret realizations of a graph on the sphere up to rotations as elements of a moduli space of curves of genus zero. We focus on those graphs that admit an assignment of edge lengths on the sphere resulting in a flexible object. Our interpretation of realizations allows us to provide a combinatorial characterization of these graphs in terms of the existence of particular colorings of the edges. Moreover, we determine necessary relations for flexibility between the spherical lengths of the edges. We conclude by classifying all possible motions on the sphere of the complete bipartite graph with 3+3 vertices where no two vertices coincide or are antipodal.

中文翻译：

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关于一般刚性图在球面上的悖论运动的存在性

SIAM Journal on Discrete Mathematics，第 35 卷，第 1 期，第 325-361 页，2021 年 1 月。
我们将球体上直至旋转的图的实现解释为属零曲线模空间的元素。我们关注那些允许在球体上分配边长的图，从而产生一个灵活的对象。我们对实现的解释使我们能够根据边的特定颜色的存在提供这些图的组合特征。此外，我们确定了边缘球形长度之间灵活性的必要关系。我们通过对具有 3+3 个顶点的完整二分图球面上的所有可能运动进行分类来得出结论，其中没有两个顶点重合或对映。