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combinatorics / Rigidity theory

Garamvölgyi-Jackson-Jordán Conjecture on Cliques in Minimally Globally Rigid Graphs

Every minimally generically globally rigid graph in $\mathbb{R}^d$ containing a subgraph isomorphic to $K_{d+2}$ is itself isomorphic to $K_{d+2}$, confirming Conjecture 6.3 of Garamvölgyi, Jackson and Jordán (2025).

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combinatoricsApr 30, 2026Significance 8/100Registry: unreviewed

Garamvölgyi-Jackson-Jordán Conjecture on Cliques in Minimally Globally Rigid Graphs

Prior state unknown→proved

Every minimally generically globally rigid graph in $\mathbb{R}^d$ containing a subgraph isomorphic to $K_{d+2}$ is itself isomorphic to $K_{d+2}$, confirming Conjecture 6.3 of Garamvölgyi, Jackson and Jordán (2025).

Source authenticatedGaramvölgyi-Jackson-Jordán Conjecture on Cliques in Minimally Globally Rigid Graphs →
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Every minimally generically globally rigid graph in $\mathbb{R}^d$ containing a subgraph isomorphic to $K_{d+2}$ is itself isomorphic to $K_{d+2}$, confirming Conjecture 6.3 of Garamvölgyi, Jackson and Jordán (2025).

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