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

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)2n3.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.

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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