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  • RoIG_2 21Feb_2022scp

    Rights statement: The final publication is available at Springer via http://dx.doi.org/10.1007/s00373-022-02486-y

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The Rigidity of Infinite Graphs II

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

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The Rigidity of Infinite Graphs II. / Kitson, Derek; Power, Stephen.
In: Graphs and Combinatorics, Vol. 38, No. 3, 83, 30.06.2022.

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

Harvard

Kitson, D & Power, S 2022, 'The Rigidity of Infinite Graphs II', Graphs and Combinatorics, vol. 38, no. 3, 83. https://doi.org/10.1007/s00373-022-02486-y

APA

Kitson, D., & Power, S. (2022). The Rigidity of Infinite Graphs II. Graphs and Combinatorics, 38(3), Article 83. https://doi.org/10.1007/s00373-022-02486-y

Vancouver

Kitson D, Power S. The Rigidity of Infinite Graphs II. Graphs and Combinatorics. 2022 Jun 30;38(3):83. Epub 2022 Apr 13. doi: 10.1007/s00373-022-02486-y

Author

Kitson, Derek ; Power, Stephen. / The Rigidity of Infinite Graphs II. In: Graphs and Combinatorics. 2022 ; Vol. 38, No. 3.

Bibtex

@article{874ca72d41ab4c448deb40284a4fe167,
title = "The Rigidity of Infinite Graphs II",
abstract = "Inductive constructions are established for countably infinite simple graphs which have minimally rigid locally generic placements in R^2. This generalises a well-known result of Henneberg for generically rigid finite graphs. Inductive methods are also employed in the determination of the infinitesimal flexibility dimension of countably infinite graphs associated with infinitely faceted convex polytopes in R^3. In particular, a generalisation of Cauchy's rigidity theorem is obtained.",
keywords = "Infinite graphs, Infinitesimal rigidity, Cauchy's rigidity theorem, Graph rigidity",
author = "Derek Kitson and Stephen Power",
note = "The final publication is available at Springer via http://dx.doi.org/10.1007/s00373-022-02486-y",
year = "2022",
month = jun,
day = "30",
doi = "10.1007/s00373-022-02486-y",
language = "English",
volume = "38",
journal = "Graphs and Combinatorics",
issn = "0911-0119",
publisher = "Springer Japan",
number = "3",

}

RIS

TY - JOUR

T1 - The Rigidity of Infinite Graphs II

AU - Kitson, Derek

AU - Power, Stephen

N1 - The final publication is available at Springer via http://dx.doi.org/10.1007/s00373-022-02486-y

PY - 2022/6/30

Y1 - 2022/6/30

N2 - Inductive constructions are established for countably infinite simple graphs which have minimally rigid locally generic placements in R^2. This generalises a well-known result of Henneberg for generically rigid finite graphs. Inductive methods are also employed in the determination of the infinitesimal flexibility dimension of countably infinite graphs associated with infinitely faceted convex polytopes in R^3. In particular, a generalisation of Cauchy's rigidity theorem is obtained.

AB - Inductive constructions are established for countably infinite simple graphs which have minimally rigid locally generic placements in R^2. This generalises a well-known result of Henneberg for generically rigid finite graphs. Inductive methods are also employed in the determination of the infinitesimal flexibility dimension of countably infinite graphs associated with infinitely faceted convex polytopes in R^3. In particular, a generalisation of Cauchy's rigidity theorem is obtained.

KW - Infinite graphs

KW - Infinitesimal rigidity

KW - Cauchy's rigidity theorem

KW - Graph rigidity

U2 - 10.1007/s00373-022-02486-y

DO - 10.1007/s00373-022-02486-y

M3 - Journal article

VL - 38

JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

SN - 0911-0119

IS - 3

M1 - 83

ER -