perfect

• 2017 Diestel2017
  • page 135 : perfect – A graph is called perfect if every induced subgraph $H \subseteq G$ has chromatic number $\chi(H)=\omega(H)$, i.e. if the trivial lower bound of $\omega(H)$ colours always suffices to colour the vertices of $H$.
• unknown
  • perfect upper bounds distance to perfect by a constant – by definition
• assumed
  • chordal upper bounds perfect by a constant
  • graph class perfect is not included in graph class chordal
  • cograph upper bounds perfect by a constant
  • graph class perfect is not included in graph class cograph
  • bipartite upper bounds perfect by a constant
  • graph class perfect is not included in graph class bipartite