distance to planar

• SchroderThesis
  • page 21 : bounded bandwidth does not imply bounded distance to planar – Proposition 3.13
  • page 21 : bounded treedepth does not imply bounded distance to planar – Proposition 3.13
  • page 23 : bounded distance to planar does not imply bounded clique-width – Proposition 3.17
  • page 33 : bounded genus does not imply bounded distance to planar – Proposition 3.34
• unknown source
  • graph class planar has constant distance to planar – by definition
  • bounded bounded components does not imply bounded distance to planar – By a disjoint union of many $K_5$ graphs.
• Tran2022
  • page 37 : distance to planar upper bounds twin-width by an exponential function – Theorem 6.4. Distance to Planar strictly upper bounds Twin-width.
  • page 37 : bounded twin-width does not imply bounded distance to planar – Theorem 6.4. Distance to Planar strictly upper bounds Twin-width.