page 7 : book thickness – A geometric drawing in which the vertices are in convex position is called a book embedding. The book thickness of a graph $G$, …, is the minimum $k \in \mathbb N$ such that there is book embedding of $G$ with thickness $k$.
page 8 : treewidth $k$ upper bounds book thickness by $\mathcal O(k)$ – The maximum book thickness … of a graph $\mathcal T_k$ (ed: $k$-tree) satisfy … $=k$ for $k \le 2$, $=k+1$ for $k \ge 3$.
page 14 : book thickness $k$ upper bounds acyclic chromatic number by $2^{\mathcal O(k)}$ – Theorem 5. Acyclic chromatic number is bounded by stack-number (ed: a.k.a. book-thickness). In particular, every $k$-stack graph $G$ has acyclich chromatic number $\chi_a(G) \le 80^{k(2k-1)}$.
book thickness – … a book embedding is a generalization of planar embedding of a graph to embeddings into a book, a collection of half-planes all having the same line as their boundary. Usually, the vertices of the graph are required to lie on this boundary line, called the spine, and the edges are required to stay within a single half-plane. The book thickness of a graph is the smallest possible number of half-planes for any book embedding of the graph.
