planar

• 2017 Diestel2017
  • page 89 : planar – When we draw a graph on a piece of paper, we naturally try to do this as transparently as possible. One obvious way to limit the mess created by all the lines is to avoid intersections. … Graphs drawn in this way are called \emph{plane graphs}; abstract graphs that can be drawn in this way are called \emph{planar}.
• unknown
  • planar upper bounds distance to planar by a constant – by definition
  • planar upper bounds genus by a constant
  • graph class planar has unbounded girth
  • graph class planar has unbounded maximum degree
  • graph class planar has unbounded distance to perfect
• assumed
  • outerplanar upper bounds planar by a constant
  • graph class planar is not included in graph class outerplanar
  • grid upper bounds planar by a constant
  • graph class planar is not included in graph class grid