15 citations · 38 across the 6 of their papers we have counts for
6 papers
Countable Graphs with Finite Path-width: Characterisation and Universality
Tony Huynh, Freddie Illingworth, Nikolai Karol +4
We study path-width and the closely related parameter line-width in countably infinite graphs. Our first result characterises the graphs of finite path-width: they are the graphs t…
Coarse Menger property of quasi-minor excluded graphs and length spaces
Chun-Hung Liu
Menger's theorem is an important building block of numerous results in the study of graph structure. We consider a variant in terms of coarse geometry. We say that a set of graphs…
Assouad-Nagata dimension of minor-closed metrics
Chun-Hung Liu
Assouad-Nagata dimension addresses both large and small scale behaviors of metric spaces and is a refinement of Gromov's asymptotic dimension. A metric space is a minor-closed…
Proper Conflict-free Coloring of Graphs with Large Maximum Degree
Daniel W. Cranston, Chun-Hung Liu
A proper coloring of a graph is \emph{conflict-free} if, for every non-isolated vertex, some color is used exactly once on its neighborhood. Caro, Petruševski, and Škrekovski prove…
Clustered Coloring of Graphs with Bounded Layered Treewidth and Bounded Degree
Chun-Hung Liu, David R. Wood
The clustering of a graph coloring is the maximum size of monochromatic components. This paper studies colorings with bounded clustering in graph classes with bounded layered treew…
Proper conflict-free list-coloring, odd minors, subdivisions, and layered treewidth
Chun-Hung Liu
Proper conflict-free coloring is an intermediate notion between proper coloring of a graph and proper coloring of its square. It is a proper coloring such that for every non-isolat…