2015/02/08 by Robert Connelly, Connelly, Robert, Steven J. Gortler +1 · 1 citation
Engineering · #52C25 #52C30 #Advanced Antenna and Metasurface Technologies #Advanced Materials and Mechanics #FOS: Mathematics #Metric Geometry (math.MG) #Structural Analysis and Optimization
paper · pdf · doi:10.48550/arxiv.1502.02278
openalex publication_date 2015/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We describe a very simple condition that is necessary for the universal rigidity of a complete bipartite framework (K(n,m),p,q). This condition is also sufficient for universal rigidity under a variety of weak assumptions, such as general position. Even without any of these assumptions, in complete generality, we extend these ideas to obtain an efficient algorithm, based on a sequence of linear programs, that determines whether an input framework of a complete bipartite graph is universally rigid or not.