The restrained-polynomial deck reconstructs the chromatic polynomial

Let $G_1$ and $G_2$ be graphs. For each vertex $v$, let $\rho_{r_v^{(2)}}(k)$ denote the corresponding restrained chromatic polynomial, and consider the multiset of these polynomials over the vertices. Restrained-deck reconstruction conjecture. If $G_1$ and $G_2$ share the same multiset

$$\{\rho_{r_v^{(2)}}(k)\}_{v\in V(G_1)}=\{\rho_{r_v^{(2)}}(k)\}_{v\in V(G_2)},$$

then $\pi_{G_1}(k)=\pi_{G_2}(k)$.

This is compared with the Polynomial Reconstruction Problem, which asks whether the chromatic polynomial can be recovered from the vertex-deletion deck. The status of this restrained-polynomial version is unclear in the paper.