Sokal's bounded-edge-connectivity conjecture for chromatic roots

Let $G$ be a graph and let $\Lambda(G)$ be the maximum number of edge-disjoint paths joining any pair of vertices of $G$. Sokal's conjecture. There exists a constant $C$ such that

$$|P(G,t)|>0$$

for every complex $t$ with

$$|t|\geq C\Lambda(G).$$

Since $\Lambda(G)\leq\Delta(G)$ and bounds the degeneracy, this would extend the known maximum-degree zero-free estimate to a broader structural parameter. The source presents the assertion as open.