The Rigidity of Infinite Graphs II

The Rigidity of Infinite Graphs II

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 infinites...

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Veröffentlicht in:Graphs and combinatorics 2022-06, Vol.38 (3), Article 83
Hauptverfasser: Kitson, D., Power, S. C.
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorics
Engineering Design
Graphs
Mathematics
Mathematics and Statistics
Original Paper
Polytopes
Rigidity
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Zusammenfassung: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.
ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-022-02486-y