Brown–Colbourn conjecture on all-terminal reliability roots

Let $G=(V,E)$ be a connected graph, and let $\mathrm{Rel}(G;q)$ denote its all-terminal reliability polynomial in the edge-failure probability $q$. A complex number $z$ is an all-terminal reliability root if $\mathrm{Rel}(G;z)=0$. Brown–Colbourn conjecture. If $z$ is a root of $\mathrm{Rel}(G;q)$, then

$$|z|\leq 1.$$

Equivalently, all all-terminal reliability roots lie in the unit disk. The conjecture is false in general, although it holds for series-parallel graphs; counterexamples were found by Sokal and Royle.