Local and global $d$-rigidity are not definable in the first order logic of graphs
Combinatorics
2025-11-11 v1 Logic
Abstract
We use Hanf locality and a result of Cruickshank, Jackson, and Tanigawa on the global rigidity of graphs of -circuits to prove that local and global -rigidity are not definable in the first order logic of graphs.
Cite
@article{arxiv.2511.05741,
title = {Local and global $d$-rigidity are not definable in the first order logic of graphs},
author = {Daniel Irving Bernstein and Nathaniel Vaduthala},
journal= {arXiv preprint arXiv:2511.05741},
year = {2025}
}