5 problems

In-dominating-set conjecture. There exists a function $f:\mathbb{N}\rightarrow\mathbb{N}$ such that, for every $k\geq1$, if

Out-leaf extension conjecture. The digraph $F^\ast$ is $\delta^+$-maderian as well.

Long-subdivision extraction conjecture. There is a function $f:\mathbb{N}\rightarrow\mathbb{N}$ such that for every $k\in\mathbb{N}$ and every digraph $D$ with

Subdivision-preservation conjecture. If a digraph $F$ is $\delta^+$-maderian, all subdivisions of $F$ are $\delta^+$-maderian as well.

Disjoint-union conjecture for oriented cycles. Any disjoint union of orientations of cycles is $\delta^+$-maderian.