recursively solve the problem on the remaining components, and then combine these solutions to obtain a solution for the original problem.

Secondly, treewidth is a key parameter in graph structure theory, especially in Robertson and Seymour’s seminal series of papers on graph minors [@RS-GraphMinors]. Ultimately, the purpose of these papers was to prove what it now known as the Graph Minor Theorem (often referred to as Wagner’s Conjecture), which states that any class of minor-closed graphs (other than the class of all graphs) has a finite set of forbidden minors. In order to prove this, Robertson and Seymour separately considered classes with bounded treewidth and classes with unbounded treewidth. The Graph Minor Theorem is (comparatively) easy to prove for classes with bounded treewidth [@RS-GraphMinorsIV-JCTB90]. In order to prove the Graph Minor Theorem for classes with unbounded treewidth, Robertson and Seymour showed that graphs with large treewidth contain large grid minors. This Grid Minor Theorem has been reproved by many researchers; we will discuss it more thoroughly in Section \[section:gridminors\]. In proving these results, the parameters *linkedness* and *well-linked number* were used. At the heart of the Graph Minor Theorem is the Graph Minor Structure Theorem, which describes how to construct 