J. Cruickshank

activity

20092023

most citedRigidity of linearly-constrained frameworks

12 citations · 19 across the 13 of their papers we have counts for

collaborators

Showing math.COShow all

10 papers · 1 filter

math.CO2023★ 1 cited

Rigidity of Symmetric Simplicial Complexes and the Lower Bound Theorem

James Cruickshank, Bill Jackson, Shinichi Tanigawa

We show that, if $Γ$ is a point group of $R^{k + 1}$ of order two for some $k \geq 2$ and $S$ is a $k$ -pseudomanifold which has a free automorphism of order two, the…

math.CO2022★ 1 cited

Global Rigidity of Line Constrained Frameworks

James Cruickshank, Fatemeh Mohammadi, Harshit J Motwani +2

We consider the global rigidity problem for bar-joint frameworks where each vertex is constrained to lie on a particular line in $R^{d}$ . In our setting we allow multiple ver…

math.CO2022★ 3 cited

Global Rigidity of Triangulated Manifolds

James Cruickshank, Bill Jackson, Shin-ichi Tanigawa

We prove that if $G$ is the graph of a connected triangulated $(d - 1)$ -manifold, for $d \geq 3$ , then $G$ is generically globally rigid in $R^{d}$ if and only if it is $(d + 1)$ -…

math.CO2021

Braced triangulations and rigidity

James Cruickshank, Eleftherios Kastis, Derek Kitson +1

We consider the problem of finding an inductive construction, based on vertex splitting, of triangulated spheres with a fixed number of additional edges (braces). We show that for…

math.CO2020

Symmetric contact systems of segments, pseudotriangulations and inductive constructions for corresponding surface graphs

James Cruickshank, Bernd Schulze

We characterise the quotient surface graphs arising from symmetric contact systems of line segments in the plane and also from symmetric pointed pseudotriangulations in the case wh…

math.CO2020

Vertex Splitting, Coincident Realisations and Global Rigidity of Braced Triangulations

James Cruickshank, Bill Jackson, Shin-ichi Tanigawa

We give a short proof of a result of Jordan and Tanigawa that a 4-connected graph which has a spanning planar triangulation as a proper subgraph is generically globally rigid in R^…

math.CO2019

Topological inductive constructions for tight surface graphs

James Cruickshank, Derek Kitson, Stephen C. Power +1

We investigate properties of sparse and tight surface graphs. In particular we derive topological inductive constructions for $(2, 2)$ -tight surface graphs in the case of the spher…

math.CO2018★ 12 cited

Rigidity of linearly-constrained frameworks

James Cruickshank, Hakan Guler, Bill Jackson +1

We consider the problem of characterising the generic rigidity of bar-joint frameworks in $R^{d}$ in which each vertex is constrained to lie in a given affine subspace. The…

math.CO2015★ 1 cited

The generic minimal rigidity of a partially triangulated torus

James Cruickshank, Derek Kitson, Stephen Power

A simple graph is $3$ -rigid if its generic bar-joint frameworks in $R^{3}$ are infinitesimally rigid. Necessary and sufficient conditions are obtained for the minimal $3$ -rigidity of…

math.CO2015

The generic rigidity of triangulated spheres with blocks and holes

James Cruickshank, Derek Kitson, Stephen Power

A simple graph G=(V,E) is 3-rigid if its generic bar-joint frameworks in R3 are infinitesimally rigid. Block and hole graphs are derived from triangulated spheres by the removal of…