2 problems

The $C_4$-factor conjecture. There exists $n_0=n_0(\eta)\in\mathbb N$ such that, for every $n\geq n_0$ divisible by $4$, if

Let $D$ be a digraph of order $n$, with minimum semi-degree $\delta^0(D)$. Let $n=n_1+\cdots+n_k$ be a positive integer partition with $n_i\geq 3$ for each $i$. A cycle factor of t…