Jackson–Owen lower-bound conjecture for realisation numbers of minimally 2-rigid graphs

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Let GG be a minimally 22-rigid graph with nn vertices, and let c2(G)c_2(G) denote its realisation number.

Jackson–Owen conjecture. Every minimally 22-rigid graph GG with nn vertices satisfies

c2(G)≥2n−3.c_2(G) \geq 2^{n-3}.

This conjecture proposes an exponential lower bound for the number of realisations of minimally 22-rigid graphs. The supplied text gives no information about whether the bound has been proved or disproved.

References

Primary source

Oliver Clarke, Sean Dewar, Daniel Green Tripp, James Maxwell, Anthony Nixon, Yue Ren and Ben Smith, “A tropical approach to rigidity: counting realisations of frameworks”, arXiv:2502.10255 (2025).

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