Maximum realization graphs for larger vertex counts

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

Background

The paper studies the maximum number of complex realizations attainable by minimally rigid graphs with a prescribed number of vertices. Complete enumeration is available only for relatively small vertex counts, while larger computations examine selected graphs and therefore cannot certify global maximality. The authors explicitly state that it is unknown whether any of the currently identified high-count graphs are actual maxima once n is at least 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, immediately after Theorem 2D lower-bound discussion