8 papers · 1 filter
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…
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…