cluster

• assumed
  • cluster upper bounds interval by a constant
  • graph class interval is not included in graph class cluster
  • cluster upper bounds block by a constant
  • graph class block is not included in graph class cluster
  • edgeless upper bounds cluster by a constant
  • graph class cluster is not included in graph class edgeless
• unknown
  • complete upper bounds cluster by a constant – by definition
  • cluster – Disjoint union of complete graphs.
  • cluster – Every connected component is a complete graph.
  • cluster – Does not include path on three vertices as an induced subgraph.
  • cluster upper bounds distance to cluster by a constant – by definition
  • cluster upper bounds twin-cover number by a constant
  • graph class cluster has unbounded domination number