Complexity for general network and subnetwork-family inputs

Determine whether CoveringNumber remains tractable or becomes intractable for general choices of an input network class and a family of subnetworks.

Background

CoveringNumber has two variable components: the input network class and the family of subnetworks to be covered. The paper studies trees with all subtrees and discusses restricted families such as tree-child or orchard subnetworks, but leaves unresolved the computational complexity for general combinations of these two inputs.

References

Finally, it would be of great interest to consider different combinations for the two inputs, to determine whether CoveringNumber remains tractable or becomes intractable for general choices of an input network and a family of subnetworks.

— 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”