Chun‐Hung Liu

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...

Clustered coloring of graphs excluding a subgraph and a minor

A graph coloring has bounded clustering if each monochromatic component has bounded size. Equivalently, it is a partition of the vertices into induced subgraphs with bounded size components. This paper studies clustered colorings of graphs, where the number of colors depends on a...