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
- chordal upper bounds perfect by a constant
- bounded perfect does not imply bounded chordal
- cograph upper bounds perfect by a constant
- bounded perfect does not imply bounded cograph
- bipartite upper bounds perfect by a constant
- bounded perfect does not imply bounded bipartite
- perfect upper bounds distance to perfect by a constant – by definition