Jackson–Owen lower-bound conjecture for realisation numbers of minimally 2-rigid graphs
Let be a minimally -rigid graph with vertices, and let denote its realisation number.
Jackson–Owen conjecture. Every minimally -rigid graph with vertices satisfies
This conjecture proposes an exponential lower bound for the number of realisations of minimally -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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