Reduction of every subtree of a tree-child network

Determine whether every subtree of a tree-child network is reducible by some cherry-picking sequence of that network.

Background

The paper shows that the tree-child covering number can be infinite when tree-child sequences are required, because some subtrees cannot be reduced by any tree-child sequence. It then asks whether allowing general cherry-picking sequences, which are more general than tree-child sequences, guarantees reducibility for every subtree of every tree-child network.

References

For the latter, one can ask if, for every subtree of~$N$, there exists a cherry-picking sequence of~$N$ which reduces it (since cherry-picking sequences are more general than tree-child sequences).

— How many cherry-picking sequences are needed to reduce all subtrees of a phylogenetic tree?  (2608.19916 - Kollmann et al., 20 Aug 2026) in Section 6, Discussion, paragraph “Open problems”