Cliques in minimally globally rigid graphs

Abstract

We show that every minimally generically globally rigid graph in ${\mathbb{R}}^d$ which contains a subgraph isomorphic to $K_{d+2}$ is itself isomorphic to $K_{d+2}$, confirming a conjecture by Garamv{ö}lgyi, Jackson, and Jord{á}n. The proof is entirely generated by ChatGPT 5.5.