path

• 2022/09 Tran2022
  • page 24 : graph class path has unbounded modular-width – The Modular-width of a path $P$ with length $n > 3$ is $n$.
  • page 26 : graph class path has unbounded neighborhood diversity – The Neighborhood Diversity of a Path $P$ with length $n > 3$ is $n$.
• 2010/08 Sasak2010
  • page 30 : path upper bounds carving-width by a constant – … path with carving-width 2.
• unknown
  • path upper bounds connected by a constant – by definition
  • path upper bounds linear forest by a constant – by definition
  • graph class path has unbounded treedepth
• assumed
  • path upper bounds tree by a constant
  • graph class tree is not included in graph class path
  • path upper bounds grid by a constant
  • graph class grid is not included in graph class path