Loebl's equivalence conjecture for the q-dichromate and U-polynomial

Let $G=(V,E)$ be a graph, let $q$ be a non-negative-integer variable, and let $x,y$ be real variables. Define the $q$-dichromate by

$$B_q(G,x,y)=\sum_{A\subseteq E}x^{|A|}\prod_{W\in\operatorname{\mathcal{C}}(A)}(y)_{q^{|W|}},$$

where $\operatorname{\mathcal{C}}(A)$ is the set of connected components of the spanning subgraph $(V,A)$, $|W|$ is the number of vertices of $W$, and $(y)_n=y(y-1)\dots(y-n+1)$. The $U$-polynomial is the graph polynomial obtained from the spanning-subgraph component-size data. Loebl's equivalence conjecture. The $q$-dichromate is equivalent to the $U$-polynomial. This would imply that the graph polynomials in the first family, which require infinitely many variables, can be represented naturally using finitely many variables.