Tree isomorphism conjecture for chromatic symmetric functions

Let $G$ and $H$ be trees, and let $\chi_G(x)$ denote the chromatic symmetric function of $G$. Tree isomorphism conjecture. If $G$ and $H$ are non-isomorphic trees, then

$$\chi_G(x)\neq\chi_H(x).$$

The conjecture asks whether the chromatic symmetric function distinguishes trees. It has been computationally verified for all trees with at most 29 vertices and for certain classes of trees, but the general statement remains open.