2 problems

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…

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.