distance to cluster

• unknown source
  • graph class cluster has constant distance to cluster – by definition
  • graph class path has unbounded distance to cluster – trivially
• Tran2022
  • page 18 : twin-cover number upper bounds distance to cluster by a linear function – … 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.
• SchroderThesis
  • page 13 : bounded distance to cluster does not imply bounded distance to co-cluster – Proposition 3.3
• assumed
  • twin-cover number upper bounds distance to cluster by a linear function – By definition