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A counter-example to Baranyai's combinatorial characterisation for 3-rigidity
Sean Dewar
Recently Baranyai described a necessary combinatorial characterisation of graph rigidity for dimension 3. In this short note we provide a counter-example to the converse of the con…
Computing the number of realisations of a rigid graph
Sean Dewar, Georg Grasegger, Josef Schicho +2
A graph is said to be rigid if, given a generic realisation of the graph as a bar-and-joint framework in the plane, there exist only finitely many other realisations of the graph w…
Algebraic connectivity in normed spaces
James Cruickshank, Sean Dewar, Derek Kitson
The algebraic connectivity of a graph in a finite dimensional real normed linear space is a geometric counterpart to the Fiedler number of the graph and can be regarded as…
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…
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…