Global Rigidity of Periodic Graphs under Fixed-lattice Representations

Kaszanitzky, Viktoria and Schulze, Bernd and Tanigawa, Shin-ichi (2021) Global Rigidity of Periodic Graphs under Fixed-lattice Representations. Journal of Combinatorial Theory, Series B, 146. pp. 176-218. ISSN 0095-8956

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In [9] Hendrickson proved that (d+1)-connectivity and redundant rigidity are necessary conditions for a generic (non-complete) bar-joint framework to be globally rigid in Rd. Jackson and Jordán [10] confirmed that these conditions are also sufficient in R2, giving a combinatorial characterization of graphs whose generic realizations in R2 are globally rigid. In this paper, we establish analogues of these results for infinite periodic frameworks under fixed lattice representations. Our combinatorial characterization of globally rigid generic periodic frameworks in R2 in particular implies toroidal and cylindrical counterparts of the theorem by Jackson and Jordán.

Item Type:
Journal Article
Journal or Publication Title:
Journal of Combinatorial Theory, Series B
Uncontrolled Keywords:
?? discrete mathematics and combinatoricscomputational theory and mathematicstheoretical computer science ??
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Deposited On:
22 Sep 2020 14:30
Last Modified:
15 May 2024 16:15