distance to linear forest

• 2019 Sorge2019
  • page 8 : maximum leaf number $k$ upper bounds distance to linear forest by $\mathcal O(k)$ – 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
  • linear forest upper bounds distance to linear forest by a constant – by definition
  • distance to linear forest $k$ upper bounds pathwidth by $\mathcal O(k)$ – 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 $k$ upper bounds pathwidth by $\mathcal O(k)$ – 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 $k$ upper bounds distance to linear forest by $f(k)$
• SchroderThesis
  • page 12 : distance to linear forest $k$ upper bounds h-index by $\mathcal O(k)$ – Proposition 3.2