Akbari–Kano conjecture on two-valued factors of odd-regular graphs

Let $r$ be a positive odd integer, let $t$ satisfy $0\leq t\leq r$, and let an $\{r-t,t\}$-factor be a spanning subgraph in which every vertex has degree either $r-t$ or $t$.

Akbari–Kano conjecture. Every $r$-regular graph has an $\{r-t,t\}$-factor.

The conjecture was disproved by Axenovich and Rollin. The paper records partial positive and negative results identifying ranges of $r$ and $t$ for which such factors must exist or can fail to exist.