distance to chordal

• Sorge2019
  • page 9 : distance to chordal upper bounds chordality by a linear function – (ed: apparently goes as the lemma for ddist to interval and boxicity) Lemma 4.16. The distance $i$ to an interval graph upper bounds the boxicity $b$. We have $b \le i+1$.
  • page 10 : feedback vertex set upper bounds distance to chordal by a linear function – Lemma 4.20. The feedback edge set number $f$ upper bounds the distance to a chordal graph $c$. We have $c \le f$.
• unknown source
  • graph class chordal has constant distance to chordal – by definition
  • graph class co-cluster has unbounded distance to chordal
  • graph class grid has unbounded distance to chordal
• SchroderThesis
  • page 20 : bounded distance to co-cluster does not imply bounded distance to chordal – Proposition 3.12
  • page 20 : bounded distance to bipartite does not imply bounded distance to chordal – Proposition 3.12
  • page 27 : bounded distance to chordal does not imply bounded boxicity – Proposition 3.25