Graph connectivity and universal rigidity of bar frameworks

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• 作者：A.Y. Alfakih ^{alfakih@uwindsor.ca}
• 关键词：Bar frameworks ; Universal rigidity ; Orthogonal representation ; Connectivity of graphs ; Stress and Gale matrices
• 刊名：Discrete Applied Mathematics
• 出版年：2017
• 出版时间：30 January 2017
• 年：2017
• 卷：217
• 期：part_P3
• 页码：707-710
• 全文大小：368 K
• 卷排序：217

文摘

Let GG be a graph on nn nodes. In this note, we prove that if GG is (r+1)(r+1)-vertex connected, 1≤r≤n−21≤r≤n−2, then there exists a configuration pp in general position in RrRr such that the bar framework (G,p)(G,p) is universally rigid. The proof is constructive, and is based on a theorem by Lovász et al concerning orthogonal representations and connectivity of graphs Lovász et al. (0000, 2000).