The Rigidity of Infinite Graphs II

Kitson, Derek and Power, Stephen (2022) The Rigidity of Infinite Graphs II. Graphs and Combinatorics, 38 (3). ISSN 0911-0119

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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.

Item Type:
Journal Article
Journal or Publication Title:
Graphs and Combinatorics
Additional Information:
The final publication is available at Springer via http://dx.doi.org/10.1007/s00373-022-02486-y
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2614
Subjects:
ID Code:
167787
Deposited By:
Deposited On:
21 Mar 2022 14:05
Refereed?:
Yes
Published?:
Published
Last Modified:
22 Nov 2022 11:16