outerplanar

• 2017 Diestel2017
  • page 115 : outerplanar – A graph is called outerplanar if it has a drawing in which every vertex lies on the boundary of the outer face.
• 1998 Bodlaender1998
  • page 34 : outerplanar upper bounds treewidth by a constant – Lemma 78. Every outerplanar graph $G=(V,E)$ has treewidth at most 2.
• assumed
  • outerplanar upper bounds planar by a constant
  • graph class planar is not included in graph class outerplanar
  • disjoint cycles upper bounds outerplanar by a constant
  • graph class outerplanar is not included in graph class disjoint cycles
• unknown
  • outerplanar upper bounds distance to outerplanar by a constant – by definition
  • outerplanar upper bounds bisection bandwidth by a constant