perfect

• assumed
  • graph class chordal is included in graph class perfect
  • graph class perfect is not included in graph class chordal
  • graph class cograph is included in graph class perfect
  • graph class perfect is not included in graph class cograph
  • graph class bipartite is included in graph class perfect
  • graph class perfect is not included in graph class bipartite
• 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 source
  • graph class perfect has constant distance to perfect – by definition