A graph G=(V, E) is planar, if it can be drawn in the plane so that its edges are Jordan curves
and they intersect only at their endnodes 1. A plane map is a planar graph with a fixed …

Chapter 61 described the basic theory of infinitesimal rigidity of bar and joint structures and
a number of related structures. In this chapter, we consider the stronger properties of: Global …

We show that a generic framework (G, p) on the cylinder is globally rigid if and only if G is a
complete graph on at most four vertices or G is both redundantly rigid and 2-connected. To …

Abstract In 2005, Bob Connelly showed that a generic framework in R^ d R d is globally rigid
if it has a stress matrix of maximum possible rank, and that this sufficient condition for …

A fundamental theorem of Laman characterises when a bar-joint framework realised
generically in the Euclidean plane admits a non-trivial continuous deformation of its vertices …

This article considers the problem of 3-dimensional genome reconstruction for single-cell
data, and the uniqueness of such reconstructions in the setting of haploid organisms. We …

We develop a rigidity theory for graphs whose vertices are constrained to lie on a cylinder
and in which two given vertices are coincident. We apply our result to show that the vertex …

We provide a constructive characterisation of circuits in the simple (2, 2)-sparsity matroid. A
circuit is a simple graph G=(V, E) with| E|= 2| V|− 1 where the number of edges induced by …

Abstract In [9] Hendrickson proved that (d+ 1)-connectivity and redundant rigidity are
necessary conditions for a generic (non-complete) bar-joint framework to be globally rigid in …

A linearly constrained framework in is a point configuration together with a system of
constraints that fixes the distances between some pairs of points and additionally restricts …