5 papers
Extremal decompositions of tropical varieties and relations with rigidity theory
Farhad Babaee, Sean Dewar, James Maxwell
Extremality and irreducibility constitute fundamental concepts in mathematics, particularly within tropical geometry. While extremal decomposition is typically computationally hard…
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…
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…
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…