The Rigidity of Infinite Graphs II

Kitson, Derek and Power, Stephen (2022) The Rigidity of Infinite Graphs II. Graphs and Combinatorics, 38 (3): 83. 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.