11 citations · 53 across the 29 of their papers we have counts for
8 papers · 1 filter
Edge-length preserving embeddings of graphs between normed spaces
Sean Dewar, Eleftherios Kastis, Derek Kitson +1
The concept of graph flattenability, initially formalized by Belk and Connelly and later expanded by Sitharam and Willoughby, extends the question of embedding finite metric spaces…
Rigid graphs in cylindrical normed spaces
Sean Dewar, Derek Kitson
We characterise rigid graphs for cylindrical normed spaces where is a finite dimensional real normed linear space and is endowed with the prod…
Infinitesimal rigidity and prestress stability for frameworks in normed spaces
Sean Dewar
A (bar-and-joint) framework is a set of points in a normed space with a set of fixed distance constraints between them. Determining whether a framework is locally rigid - i.e. whet…
Generalised rigid body motions in non-Euclidean planes with applications to global rigidity
Sean Dewar, Anthony Nixon
A bar-joint framework in a (non-Euclidean) real normed plane is the combination of a finite, simple graph and a placement of the vertices in . A framework $(…
Homothetic packings of centrally symmetric convex bodies
Sean Dewar
A centrally symmetric convex body is a convex compact set with non-empty interior that is symmetric about the origin. Of particular interest are those that are both smooth and stri…
Which graphs are rigid in ?
Sean Dewar, Derek Kitson, Anthony Nixon
We present three results which support the conjecture that a graph is minimally rigid in -dimensional -space, where and , if and only if it is…
Infinitesimal rigidity in normed planes
Sean Dewar
We prove that a graph has an infinitesimally rigid placement in a non-Euclidean normed plane if and only if it contains a -tight spanning subgraph. The method uses an induct…
Equivalence of continuous, local and infinitesimal rigidity in normed spaces
Sean Dewar
We present a rigorous study of framework rigidity in general finite dimensional normed spaces from the perspective of Lie group actions on smooth manifolds. As an application, we p…