Linear min-max relation between the treewidth of H-minor-free graphs and its largest grid

Ken-Ichi Kawarabayashi & Yusuke Kobayashi
A key theorem in algorithmic graph-minor theory is a 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. In 2008, Demaine and Hajiaghayi proved a remarkable linear min-max relation for graphs excluding any fixed minor H: every H-minor-free graph of treewidth at least c_H...