In graph theory, as well as in 3-manifold topology, there exist several width-type parameters to describe how "simple" or "thin" a given graph or 3-manifold is. These parameters, such as pathwidth or treewidth for graphs, or the concept of thin position for 3-manifolds, play an important role when studying algorithmic problems; in particular, there is a variety of problems in computational 3-manifold topology - some of them known to be computationally hard in general - that become solvable in polynomial time as soon as the dual graph of the input triangulation has bounded treewidth. In view of these algorithmic results, it is natural to ask whether every 3-manifold admits a triangulation of bounded treewidth. We show that this is not the case, i.e., that there exists an infinite family of closed 3-manifolds not admitting triangulations of bounded pathwidth or treewidth (the latter implies the former, but we present two separate proofs). We derive these results from work of Agol, of Scharlemann and Thompson, and of Scharlemann, Schultens and Saito by exhibiting explicit connections between the topology of a 3-manifold M on the one hand and width-type parameters of the dual graphs of triangulations of M on the other hand, answering a question that had been raised repeatedly by researchers in computational 3-manifold topology. In particular, we show that if a closed, orientable, irreducible, non-Haken 3-manifold M has a triangulation of treewidth (resp. pathwidth) k then the Heegaard genus of M is at most 18(k+1) (resp. 4(3k+1)).

翻译：在图形学中, 以及3 张式地形学中, 有一些宽度类型参数可以描述“ 简单” 或“ 深度” 一个特定图表或 3 张式图。 这些参数, 如图的路径或树线, 或3 张式图的薄位置概念, 在研究算法问题时起着重要作用 ; 特别是, 在计算3 张式表层( 有些已知在一般情况下是难以计算 的) 中, 有各种各样的问题 。 当输入三角图的双向图解将树线捆绑起来时, 就会在多张式图解时, 就会被解开来。 从这些3张式图中, 3张式图层和3张式图层图解的双层计算结果 。 我们从这些3张式图解的双层图解中, 3 手式图解的3 和树形图解的双层图解的图解 3 。 在Skontural 3 3 3 和图解的图解中, 我们用两个不同的图解的图解的图解的图解显示了这些图解的图解的图解 。