4 problems

Mynhardt–Roux's conjecture. For every $n\geq3$, $P_n$ is not an $\operatorname{IR}$-graph, and for every $n\geq5$, $C_n$ is not an $\operatorname{IR}$-graph.

Let $d$ be an integer greater than $1$. For each $n$, let $A_{n,d}$ (respectively, $B_{n,d}$) be the set, up to isomorphism, of all minimally $d$-rigid graphs with $n$ vertices and…

For each integer $d>1$, let $\alpha_d$ denote the corresponding asymptotic growth constant for $d$-realisation numbers. Positivity conjecture. For every $d>1$ we have … The conject…

Let $G$ be a minimally $2$-rigid graph, and let $c_2(G)$ denote its $2$-realisation number. Lower-bound conjecture. … If true, this would improve the upper bound for the asymptotic…