The 5-regular graph {4,1}-factor conjecture

A graph is 5-regular if every vertex has degree $5$, and an $\{4,1\}$-factor is a spanning subgraph in which every vertex has degree either $4$ or $1$.

5-regular $\{4,1\}$-factor conjecture. Every $5$-regular graph has an $\{4,1\}$-factor.

This is the first case of the Akbari–Kano conjecture not addressed by the preceding theorem in the paper. The supplied text does not state whether this particular case has been resolved, so its database status remains open.