Li et al.'s log-concavity 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 $\zeta(H,x)$ be the Clar covering polynomial of $H$.

Li et al.'s conjecture. The polynomial $\zeta(H,x)$ is log-concave.

Since the coefficients of $\zeta(H,x)$ are positive, this is stronger than the unimodality conjecture for Clar covering polynomials. The conjecture was proposed after extensive numerical testing and remains open in the supplied source.