distance to linear forest

• SchroderThesis
  • page 12 : distance to linear forest upper bounds h-index by a linear function – Proposition 3.2
• Sorge2019
  • page 8 : maximum leaf number upper bounds distance to linear forest by a linear function – Lemma 4.10 ([14]). The max-leaf number $\mathrm{ml}$ upper bounds the distance to disjoint paths $d$. We have $d \le \mathrm{ml}-1$.
• unknown source
  • graph class linear forest has constant distance to linear forest – by definition
  • distance to linear forest upper bounds pathwidth by a linear function – After removal of $k$ vertices the remaining class has a bounded width $w$. So by including the removed vertices in every bag, we can achieve decomposition of width $w+k$
  • distance to linear forest upper bounds pathwidth by a linear function – After removal of $k$ vertices the remaining class has a bounded width $w$. So by including the removed vertices in every bag, we can achieve decomposition of width $w+k$
  • maximum leaf number upper bounds distance to linear forest by a computable function