Sebastian Wiederrecht

Bounds on Treewidth via Excluding Disjoint Unions of Cycles

One of the fundamental results in graph minor theory is that for every planar graph $H$, there is a minimum integer $f(H)$ such that graphs with no minor isomorphic to~$H$ have treewidth at most $f(H)$. The best bound known for an arbitrary planar $H$ is ${O(|V(H)|^9\operatorname...