4 problems

Fleischner–Jackson–Litsyn–Swart's conjecture. Either $k=2$ and $G$ is a cycle, or $k=3$ and $G$ can be obtained from $K_{3,3}$ and the Heawood graph $H_0$ by repeated star products…

Let $G$ be a graph of order at least three, and write $\omega(G\setminus S)$ for the number of components of $G\setminus S$. A connected $\\{2,4\\}$-factor is a connected spanning…

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

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