Zhang's depth-two shortest cycle cover conjecture

A cycle cover of a graph is a collection of cycles covering every edge. The depth of an edge in a cycle cover is the number of cycles containing it, and the depth of the cover is the maximum edge depth. A shortest cycle cover is one of minimum total length. Zhang's depth-two conjecture. Every $3$-edge-connected graph $G$ admits a shortest cycle cover of depth $2$.

This conjecture would imply the equality conjecture relating $scc(G)$ and $T(G)$ in the paper. It remains open.