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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

Published
Article number83
<mark>Journal publication date</mark>30/06/2022
<mark>Journal</mark>Graphs and Combinatorics
Issue number3
Volume38
Publication StatusPublished
Early online date13/04/22
<mark>Original language</mark>English

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.

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