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math.CO2021
Braced triangulations and rigidity
James Cruickshank, Eleftherios Kastis, Derek Kitson +1
We consider the problem of finding an inductive construction, based on vertex splitting, of triangulated spheres with a fixed number of additional edges (braces). We show that for…
math.CO2019
Topological inductive constructions for tight surface graphs
James Cruickshank, Derek Kitson, Stephen C. Power +1
We investigate properties of sparse and tight surface graphs. In particular we derive topological inductive constructions for -tight surface graphs in the case of the spher…
math.CO2015
The generic rigidity of triangulated spheres with blocks and holes
James Cruickshank, Derek Kitson, Stephen Power
A simple graph G=(V,E) is 3-rigid if its generic bar-joint frameworks in R3 are infinitesimally rigid. Block and hole graphs are derived from triangulated spheres by the removal of…