Showing 2026Show all
3 papers · 1 filter
math.CO2026
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…
math.DG2026
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…
math.CO2026
The -dimensional realisation number of a rigid graph
Sean Dewar, Anthony Nixon, Ben Smith
Determining the number of (complex) realisations of a rigid graph for a specific choice of edge lengths is a fundamental problem in discrete geometry. In this article we provide tw…