page 3 : thickness – The thickness of a graph $G$, …, is the minimum number of planar subgraphs that partition (ed: edges of) $G$.
page 4 : treewidth $k$ upper bounds thickness by $\mathcal O(k)$ – Proposition 1. The maximum thickness of a graph in $\mathcal T_k$ (ed: $k$-tree) is $\lceil k/2 \rceil$; …