Connected 3-edge-colorable spanning-minor conjecture

A cubic graph is a graph in which every vertex has degree three. A cubic graph is 3-edge-colorable if its edges admit a proper coloring with three colors. A cubic graph $H$ is a spanning minor of a cubic graph $G$ if some subdivision of $H$ is a spanning subgraph of $G$. A $6$-even-subgraph double cover is a double cover consisting of six even subgraphs.

Connected 3-edge-colorable spanning-minor conjecture. If a cubic bridgeless graph contains a connected 3-edge-colorable cubic graph as a spanning minor, then $G$ has a $6$-even-subgraph double cover.

The source presents this as a strengthening of several earlier sufficient conditions, including those involving Kotzig and semi-Kotzig graphs. It is stated as a conjecture and no resolution is given in the paper.