The existence of Kotzig-frames in cyclically 4-edge-connected cubic graphs

A cubic graph is a graph in which every vertex has degree $3$. A graph is cyclically $4$-edge connected if no edge cut of fewer than four edges separates two subgraphs each containing a cycle. A Kotzig graph is a cubic graph admitting a proper $3$-edge-coloring such that each bicolored cycle is hamiltonian. For a $2$-connected cubic graph $G$, a Kotzig-frame is a spanning subgraph $F$ such that every component of $F$ has an even number of vertices and every component is either a cycle or a subdivision of a Kotzig graph.

Kotzig-frame existence conjecture. Every cyclically $4$-edge connected cubic graph has a Kotzig-frame.

The paper notes that no cyclically $4$-edge connected cubic graph without a Kotzig-frame was known at the time. A Kotzig-frame can yield a cycle double cover under additional conditions, so establishing the conjecture would support the cycle double cover program.