vertex integrity
- unknown
- vertex integrity $k$ upper bounds treedepth by $\mathcal O(k)$ – First, treedepth removes vertices of the modulator, then it iterates through remaining components one by one.
- vertex integrity is equal to distance to bounded components – By definition
- vertex integrity – Minimum $k$ such that there exists $k$ vertices whose removal results in connected components of sizes at most $k$.
- bounded stars does not imply bounded vertex integrity