bounded components

• unknown
  • bounded components $k$ upper bounds distance to bounded components by $\mathcal O(k)$ – by definition
  • bounded components $k$ upper bounds cutwidth by $k^{\mathcal O(1)}$ – By greedily placing one component after another.
  • bounded bounded components does not imply bounded distance to perfect – By a disjoint union of small components with distance to perfect at least 1.
  • bounded bounded components does not imply bounded distance to planar – By a disjoint union of many $K_5$ graphs.
  • edgeless upper bounds bounded components by a constant – By definition
  • bounded components $k$ upper bounds maximum degree by $\mathcal O(k)$ – By definition