Weak oddness versus resistance conjecture

Let $G$ be a bridgeless cubic graph. Let $\omega'(G)$ denote its weak oddness and $r(G)$ its resistance, using the definitions in the paper.

Weak oddness versus resistance conjecture. One has

$$\omega'(G)\leq 2r(G).$$

This conjecture compares two structural measures of edge-uncolorability. The paper presents it as one of two conjectural inequalities and gives no resolution.