page 16 : chordality – The chordality of a graph $G$ is the minimum amount of chordal graphs required, such that their intersection (ed: fixed typo) results in $G$.
page 30 : bounded modular-width does not imply bounded chordality – Theorem 4.16. Modular-width is incomparable to Chordality.
page 30 : bounded chordality does not imply bounded modular-width – Theorem 4.16. Modular-width is incomparable to Chordality.
page 9 : boxicity $k$ upper bounds chordality by $\mathcal O(k)$ – Lemma 4.15 ([8,11]). The boxicity $b$ upper-bounds the chordality $c$. We have $c \le b$.
page 9 : distance to chordal $k$ upper bounds chordality by $\mathcal O(k)$ – (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 1 : chordality – The \emph{chordality} of a graph $G=(V,E)$ is defined as the minimum $k$ such that we can write $E=E_1,\cap\dots\cap E_k$ with each $(V,E_i)$ a chordal graph.
page 2 : chromatic number $k$ upper bounds chordality by $\mathcal O(k)$ – Corollary 4. For any graph $G$, $\mathrm{Chord}(G) \le \chi(G)$, the chromatic number of $G$.
page 5 : treewidth $k$ upper bounds chordality by $\mathcal O(k)$ – Theorem 7. For any graph $G$, $\mathrm{Chord}(G) \le \tau(G)$.
