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Global Rigidity of Periodic Graphs under Fixed-lattice Representations

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Global Rigidity of Periodic Graphs under Fixed-lattice Representations. / Kaszanitzky, Viktoria; Schulze, Bernd; Tanigawa, Shin-ichi.
In: Journal of Combinatorial Theory, Series B, Vol. 146, 01.01.2021, p. 176-218.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Kaszanitzky, V, Schulze, B & Tanigawa, S 2021, 'Global Rigidity of Periodic Graphs under Fixed-lattice Representations', Journal of Combinatorial Theory, Series B, vol. 146, pp. 176-218. https://doi.org/10.1016/j.jctb.2020.09.009

APA

Kaszanitzky, V., Schulze, B., & Tanigawa, S. (2021). Global Rigidity of Periodic Graphs under Fixed-lattice Representations. Journal of Combinatorial Theory, Series B, 146, 176-218. https://doi.org/10.1016/j.jctb.2020.09.009

Vancouver

Kaszanitzky V, Schulze B, Tanigawa S. Global Rigidity of Periodic Graphs under Fixed-lattice Representations. Journal of Combinatorial Theory, Series B. 2021 Jan 1;146:176-218. Epub 2020 Sept 24. doi: 10.1016/j.jctb.2020.09.009

Author

Kaszanitzky, Viktoria ; Schulze, Bernd ; Tanigawa, Shin-ichi. / Global Rigidity of Periodic Graphs under Fixed-lattice Representations. In: Journal of Combinatorial Theory, Series B. 2021 ; Vol. 146. pp. 176-218.

Bibtex

@article{17ea0a9968ca4ddab358fb3306e4698b,
title = "Global Rigidity of Periodic Graphs under Fixed-lattice Representations",
abstract = "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 Jord{\'a}n [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 Jord{\'a}n.",
author = "Viktoria Kaszanitzky and Bernd Schulze and Shin-ichi Tanigawa",
year = "2021",
month = jan,
day = "1",
doi = "10.1016/j.jctb.2020.09.009",
language = "English",
volume = "146",
pages = "176--218",
journal = "Journal of Combinatorial Theory, Series B",
issn = "0095-8956",
publisher = "Academic Press Inc.",

}

RIS

TY - JOUR

T1 - Global Rigidity of Periodic Graphs under Fixed-lattice Representations

AU - Kaszanitzky, Viktoria

AU - Schulze, Bernd

AU - Tanigawa, Shin-ichi

PY - 2021/1/1

Y1 - 2021/1/1

N2 - 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.

AB - 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.

U2 - 10.1016/j.jctb.2020.09.009

DO - 10.1016/j.jctb.2020.09.009

M3 - Journal article

VL - 146

SP - 176

EP - 218

JO - Journal of Combinatorial Theory, Series B

JF - Journal of Combinatorial Theory, Series B

SN - 0095-8956

ER -