The poor-edge conjecture for bridgeless cubic graphs

Let $G$ be a bridgeless cubic graph, and let $P_{10}$ be the Petersen graph. Let $P_{10}^{\Delta}$ be the graph obtained from $P_{10}$ by truncating one vertex. In a normal $5$-edge-coloring, a poor edge is an edge whose endpoints together are incident with exactly three colors.

Poor-edge conjecture. If $G\not=P_{10}$, then $G$ has a normal $5$-edge-coloring with at least one poor edge. Moreover, if additionally $G\not=P_{10}^{\Delta}$, then $G$ has a normal $5$-edge-coloring with at least $6$ poor edges.

The conjecture concerns the number of poor edges guaranteed in normal $5$-edge-colorings of bridgeless cubic graphs. The paper states that its construction confirms the conjecture for the class of snarks considered, while the supplied text does not establish the claim for all bridgeless cubic graphs.