distance to planar

• 2022/09 Tran2022
  • page 37 : distance to planar $k$ upper bounds twin-width by $2^{\mathcal O(k)}$ – 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.
• unknown
  • planar upper bounds distance to planar by a constant – by definition
  • bounded bounded components does not imply bounded distance to planar – By a disjoint union of many $K_5$ graphs.
• 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