The regular edge-connected cycle cover conjecture

Let $k$ be an integer, and let $G$ be a $k$-regular, $(k-1)$-edge-connected graph. A cycle $(k-1)$-cover is a list of cycles in $G$ in which every edge appears exactly $k-1$ times.

Regular edge-connected cycle cover conjecture. There exists a cycle $(k-1)$-cover of $G$.

The paper presents this as a suspected extension of its technique to cycle $k$-covers. No resolution is given, so the statement remains open.