distance to perfect

• 2022/09 Tran2022
  • page 29 : bounded edge clique cover number does not imply bounded distance to perfect – Proposition 4.15. Edge Clique Cover Number is incomparable to Distance to Perfect.
  • page 29 : bounded distance to perfect does not imply bounded edge clique cover number – Proposition 4.15. Edge Clique Cover Number is incomparable to Distance to Perfect.
• SchroderThesis
  • page 15 : bounded clique cover number does not imply bounded distance to perfect – Proposition 3.6
  • page 19 : bounded distance to perfect does not imply bounded chordality – Proposition 3.11
  • page 26 : bounded distance to outerplanar does not imply bounded distance to perfect – Proposition 3.23
  • page 26 : bounded bandwidth does not imply bounded distance to perfect – Proposition 3.24
  • page 26 : bounded genus does not imply bounded distance to perfect – Proposition 3.24
  • page 26 : bounded treedepth does not imply bounded distance to perfect – Proposition 3.24
• unknown
  • perfect upper bounds distance to perfect by a constant – by definition
  • graph class planar has unbounded distance to perfect
  • graph class disjoint cycles has unbounded distance to perfect
  • bounded bounded components does not imply bounded distance to perfect – By a disjoint union of small components with distance to perfect at least 1.