Zhang and Zhang's unimodality conjecture for Clar covering polynomials

Let $H$ be a hexagonal system, meaning a 2-connected finite plane graph whose interior faces are regular hexagons of side length one. Let $R(H)$ be the resonance graph of $H$, and let $C(R(H),x)$ be its cube polynomial; equivalently, let $\zeta(H,x)$ denote the Clar covering polynomial of $H$.

Zhang and Zhang's conjecture. The polynomial

$$C(R(H),x)=\zeta(H,x)$$

is unimodal.

This conjecture concerns resonance graphs of hexagonal systems, a subclass of median graphs. The corresponding conjecture for all median graphs is false, but this restricted conjecture remains open.