Algorithmic Graph Minor Theory: Improved Grid Minor Bounds and Wagner’s Contraction

We explore three important avenues of research in algorithmic graph-minor theory, which all stem from a key min-max relation between the treewidth of a graph and its largest grid minor. This min-max relation is a keystone of the Graph Minor Theory of Robertson and Seymour, which ultimately proves Wagner’s Conjecture about the structure of minor-closed graph properties.