K4-minor conjecture for negative coefficients of graph independence Rayleigh differences

Let $\mathsf G$ be a graph and let $e,f$ be edges of $\mathsf G$. Write $\Delta Z(\mathbf I\mathsf G)\{e,f\}$ for the Rayleigh difference of the independence-set partition function. K4-minor conjecture. If this polynomial has a negative coefficient, then $\mathsf G$ has a $\mathsf K_4$-minor in which the images of $e$ and $f$ occur on nonadjacent edges. The conjecture implies the adjacent-edge coefficient conjecture and remains open in the source.