Note: A sufficient connectivity condition for generic rigidity in the plane
Discrete Applied Mathematics
Uniqueness of Low-Rank Matrix Completion by Rigidity Theory
SIAM Journal on Matrix Analysis and Applications
The rigidity transition in random graphs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Highly connected molecular graphs are rigid in three dimensions
Information Processing Letters
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Laman's characterization of minimally rigid 2-dimensional generic frameworks gives a matroid structure on the edge set of the underlying graph, as was first pointed out and exploited by L. Lovász and Y. Yemini. Global rigidity has only recently been characterized by a combination of two results due to T. Jordán and the first named author, and R. Connelly, respectively. We use these characterizations to investigate how graph theoretic properties such as transitivity, connectivity and regularity influence (2-dimensional generic) rigidity and global rigidity and apply some of these results to reveal rigidity properties of random graphs. In particular, we characterize the globally rigid vertex transitive graphs, and show that a random d-regular graph is asymptotically almost surely globally rigid for all d ≥ 4. © 2006 Wiley Periodicals, Inc. J Graph Theory 54: 154–166, 2007