Cliques in minimally globally rigid graphs

TL;DR

This paper proves a conjecture about the structure of minimally globally rigid graphs in Euclidean space, showing that certain subgraph conditions imply the entire graph's structure, with the proof generated by ChatGPT 5.5.

Contribution

It confirms a conjecture relating subgraph isomorphism to the entire graph's structure in minimally globally rigid graphs, using AI-generated proof.

Findings

Minimally globally rigid graphs with a $K_{d+2}$ subgraph are isomorphic to $K_{d+2}$.

The proof was entirely generated by ChatGPT 5.5.

The result advances understanding of graph rigidity in Euclidean spaces.

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{\"o}lgyi, Jackson, and Jord{\'a}n. The proof is entirely generated by ChatGPT 5.5.