2021/07/08 by James Cruickshank, Eleftherios Kastis, Cruickshank, James +5
Computer Science · Engineering · Mathematics · #05C10 #46B20 #52C25 #Advanced Materials and Mechanics #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2107.03829
openalex publication_date 2021/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 any positive integer b there is such an inductive construction of triangulations with b braces, having finitely many base graphs. In particular we establish a bound for the maximum size of a base graph with b braces that is linear in b. In the case that b=1 or 2 we determine the list of base graphs explicitly. Using these results we show that doubly braced triangulations are (generically) minimally rigid in two distinct geometric contexts arising from a hypercylinder in ℝ4 and a class of mixed norms on ℝ3.