Jackson–Owen lower-bound conjecture for realisation numbers of minimally 2-rigid graphs
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.
Sources & referencesView supporting material
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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