Covering number of general non-binary trees

Determine the covering number of general non-binary phylogenetic trees beyond the survival covering variant.

Background

The paper derives recursive formulas for the survival covering number of non-binary trees, but does not obtain a corresponding formula for the ordinary covering number. The authors identify determining the ordinary covering number for general non-binary trees as the most immediate unresolved problem and note that only loose bounds are available even for star phylogenetic trees.

References

The most immediate open problem is to determine the covering number of general non-binary trees, beyond the surviving variant.

— 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”