distance to cluster

• 2022/09 Tran2022
  • page 18 : twin-cover number $k$ upper bounds distance to cluster by $\mathcal O(k)$ – … graph $H$ with a twin cover of size $k$ has a distance to cluster of at most $k$.
  • page 18 : bounded distance to cluster does not imply bounded twin-cover number – We show that twin cover number is not upper bounded by distance to cluster.
  • page 28 : bounded modular-width does not imply bounded distance to cluster – Proposition 4.10. Modular-width is incomparable to Distance to Cluster.
  • page 28 : bounded distance to cluster does not imply bounded modular-width – Proposition 4.10. Modular-width is incomparable to Distance to Cluster.
• unknown
  • cluster upper bounds distance to cluster by a constant – by definition
  • twin-cover number $k$ upper bounds distance to cluster by $\mathcal O(k)$ – By definition
• SchroderThesis
  • page 13 : bounded distance to cluster does not imply bounded distance to co-cluster – Proposition 3.3