8 顶点刚性图欧几里得嵌入的上界
计算几何
2014-10-24 v2
摘要
如果一个图对于任何足够通用的边长选择，在模去刚性变换后，只能以有限种不同的方式嵌入到 中，则称该图在 中是（通用）刚性的。在此，我们致力于确定具有 8 个顶点的最小刚性图在平面上的最大欧几里得嵌入数问题，因为这是平面上尚未解决的最小情形。
引用
@article{arxiv.1204.6527,
title = {An upper bound on Euclidean embeddings of rigid graphs with 8 vertices},
author = {Stylianos C. Despotakis and Ioannis Z. Emiris},
journal= {arXiv preprint arXiv:1204.6527},
year = {2014}
}
备注
This paper has been withdrawn by the authors because there was a bug in the code used to produce the sub-systems in Section 4. More specifically some of the sub-systems don't satisfy the Laman property. For an update on this problem, see arXiv:1402.1484