Maximum realization graphs beyond 14 vertices

Determine whether the currently known minimally rigid graphs with the largest numbers of complex realizations are maximal for any number of vertices n greater than or equal to 15.

Background

The paper reports computationally identified graphs with currently largest known realization counts, but exhaustive enumeration becomes infeasible as the number of vertices increases. Consequently, the authors explicitly state that they do not know whether these examples attain the true maximum for any n≥15.

References

Still, we do not know whether we even found the graphs with the maximum number of realizations for any n 15.

— Explorations on the number of realizations of minimally rigid graphs  (2502.04736 - Grasegger, 7 Feb 2025) in Section 2, subsection “Realizations in the plane”