Bollobás–Pebody–Riordan conjecture on almost-complete chromatic polynomials

Let $\mathbb{G}(n,p(n))$ be the random graph model in which graphs of order $n$ are sampled with edge probability $p(n)$. A graph polynomial is almost complete when asymptotically almost all graphs in the specified model are uniquely determined by that polynomial.

Bollobás–Pebody–Riordan conjecture. For the model with $p(n)=1/2$, the chromatic polynomial is almost complete.

The source attributes this conjecture to Bollobás, Pebody and Riordan and states that, although it was proposed about 25 years earlier, it now seems unlikely; no resolution is given in the supplied text.