Coefficient lower bound for connected bridgeless cubic graphs

Determine whether, for every connected bridgeless cubic graph G, the inequality b_i ≤ |c_i| holds for the absolute value |c_i| of each coefficient c_i of the flow polynomial F(G,t), where b_i is the corresponding coefficient of (t+1)(t+2)^{n/2}.

Background

The paper proves the inequality b_i ≤ |c_i| for connected bridgeless cubic graphs whose flow polynomials have only real flow roots. The lower-bound polynomial in that result is (t+1)(t+2)^{n/2}, and the bound is shown to be attainable for specific examples. The authors leave unresolved whether the same coefficientwise lower bound holds for all connected bridgeless cubic graphs, without the assumption that all flow roots are real.