11 citations · 53 across the 29 of their papers we have counts for
32 papers
On rigidity properties of unit-distance graphs
Sean Dewar, Georg Grasegger, Alison La Porta +2
A unit-distance graph is a graph which admits a realisation in Euclidean space in which every edge has unit length. Imposing further geometric conditions on the non-edges gives a f…
Rigidity on compact surfaces through hyperbolic symmetries
Sean Dewar, Alison La Porta, Rebecca Monks +3
Generically the rigidity of bar-joint structures admits combinatorial characterisations in the Euclidean plane and, more generally, for frameworks on the sphere and the torus. The…
Generalised Erdős distance theory on graphs
Sean Dewar, Nora Frankl, Samuel Mansfield +3
The famous Erdős distinct distances problem asks the following: how many distinct distances must exist between a set of points in the plane? There are many generalisations of t…
Triangulated spheres with holes in triangulated surfaces
Katie Clinch, Sean Dewar, Niloufar Fuladi +6
Let denote a sphere with holes. Given a triangulation of a surface , we consider the question of when contains a spanning subgraph such t…
Constructing reflection-symmetric flexible realisations of graphs
Sean Dewar, Georg Grasegger, Jan Legerský
We study reflection-symmetric realisations of symmetric graphs in the plane that allow a continuous symmetry and edge-length preserving deformation. To do so, we identify a necessa…
Single-cell 3D genome reconstruction in the haploid setting using rigidity theory
Sean Dewar, Georg Grasegger, Kaie Kubjas +2
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 c…
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…
Angular constraints on planar frameworks
Sean Dewar, Georg Grasegger, Anthony Nixon +4
Consider a collection of points in the plane and the sets of slopes or directions of the lines between pairs of points. It is known that the algebraic matroid on the set of directi…
Rigidity of nearly planar classes of graphs
Sean Dewar, Georg Grasegger, Eleftherios Kastis +2
We explore the rigidity of generic frameworks in 3-dimensions whose underlying graph is close to being planar. Specifically we consider apex graphs, edge-apex graphs and their vari…
Rigid frameworks with dilation constraints
Sean Dewar, Anthony Nixon, Andrew Sainsbury
We consider the rigidity and global rigidity of bar-joint frameworks in Euclidean -space under additional dilation constraints in specified coordinate directions. In this settin…
The number of realisations of a rigid graph in Euclidean and spherical geometries
Sean Dewar, Georg Grasegger
A graph is -rigid if for any generic realisation of the graph in (equivalently, the -dimensional sphere ), there are only finitely many non-congr…
On the uniqueness of collections of pennies and marbles
Sean Dewar, Georg Grasegger, Kaie Kubjas +2
In this note we study the uniqueness problem for collections of pennies and marbles. More generally, consider a collection of unit -spheres that may touch but not overlap. Given…
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…
Identifying contact graphs of sphere packings with generic radii
Sean Dewar
Ozkan et al. conjectured that any packing of spheres with generic radii will be stress-free, and hence will have at most contacts. In this paper we prove that this conje…
Computing maximum likelihood thresholds using graph rigidity
Daniel Irving Bernstein, Sean Dewar, Steven J. Gortler +3
The maximum likelihood threshold (MLT) of a graph is the minimum number of samples to almost surely guarantee existence of the maximum likelihood estimate in the corresponding…
How many contacts can exist between oriented squares of various sizes?
Sean Dewar
A homothetic packing of squares is any set of various-size squares with the same orientation where no two squares have overlapping interiors. If all squares have the same size…
Uniquely realisable graphs in analytic normed planes
Sean Dewar, John Hewetson, Anthony Nixon
A bar-joint framework in the Euclidean space is globally rigid if it is the unique realisation, up to rigid congruences, of in with the ed…
Graph rigidity properties of Ramanujan graphs
Sebastian M. Cioabă, Sean Dewar, Georg Grasegger +1
A recent result of Cioabă, Dewar and Gu implies that any -regular Ramanujan graph with is globally rigid in . In this paper, we extend these results and…
Quotient graphs of symmetrically rigid frameworks
Sean Dewar, Georg Grasegger, Eleftherios Kastis +1
A natural problem in combinatorial rigidity theory concerns the determination of the rigidity or flexibility of bar-joint frameworks in that admit some non-trivial s…
Classifying the globally rigid edge-transitive graphs and distance-regular graphs in the plane
Sean Dewar
A graph is said to be globally rigid if almost all embeddings of the graph's vertices in the Euclidean plane will define a system of edge-length equations with a unique (up to isom…
Coincident-point rigidity in normed planes
Sean Dewar, John Hewetson, Anthony Nixon
A bar-joint framework is the combination of a graph and a map assigning positions, in some space, to the vertices of . The framework is rigid if every edge-lengt…
Flexing infinite frameworks with applications to braced Penrose tilings
Sean Dewar, Jan Legerský
A planar framework -- a graph together with a map of its vertices to the plane -- is flexible if it allows a continuous deformation preserving the distances between adjacent vertic…
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 $(…