Treewidth order conjecture for token graphs of trees

Let $G$) be a tree on $n$ vertices, and let $F_k(G)$ denote its $k$-token graph, whose vertices are the $k$-subsets of $V(G)$. For a fixed integer $k$ satisfying $1\le k\le n-1$, the treewidth order conjecture for token graphs of trees.

$$\operatorname{tw}(F_k(G)) \in \Theta(n^{k-1}).$$

This extends the established order of growth for token graphs of stars and paths to all trees. The conjecture is presented as open in the source.