The Rigidity of Infinite Graphs

A rigidity theory is developed for countably infinite simple graphs in R d . Generalisations are obtained for the Laman combinatorial characterisation of generic infinitesimal rigidity for finite graphs in R 2 and Tay’s multi-graph characterisation of generic infinitesimal rigidity for finite body-b...

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Veröffentlicht in:	Discrete & computational geometry 2018-10, Vol.60 (3), p.531-557
Hauptverfasser:	Kitson, Derek, Power, Stephen C.
Format:	Artikel
Sprache:	eng
Schlagworte:	Combinatorial analysis Combinatorics Computational Mathematics and Numerical Analysis Graphs Mathematics Mathematics and Statistics Norms Rigidity
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Beschreibung
Zusammenfassung:	A rigidity theory is developed for countably infinite simple graphs in R d . Generalisations are obtained for the Laman combinatorial characterisation of generic infinitesimal rigidity for finite graphs in R 2 and Tay’s multi-graph characterisation of generic infinitesimal rigidity for finite body-bar frameworks in R d . Analogous results are obtained for the classical non-Euclidean ℓ q norms.
ISSN:	0179-5376 1432-0444
DOI:	10.1007/s00454-018-9993-0