11 papers · 1 filter
List coloring -free planar graphs with a sparse matching of restricted lists
Stephen G. Hartke, Yupei Li, Joseph Pappe +3
A graph is -choosable if it has a proper coloring for every -list assignment. While every -free planar graph is -choosable, some of them are not -choosable, as…
DP vertex-arboricity of sparse graphs
Peter Bradshaw, Alexandr Kostochka, Zimu Xiang
The vertex arboricity of a multigraph is the minimum number for which can be partitioned into subsets, each of which induces an acyclic subgraph…
An introduction to equitable DP coloring of graphs
H. A. Kierstead, Alexandr Kostochka, Zimu Xiang
A proper -coloring of vertices of an -vertex graph is equitable if the size of every color class is or . An extension of it to list col…
On Relative Ordered Turán Density
Dylan King, Bernard Lidický, Minghui Ouyang +3
For an ordered graph , denote the Turán density by . The relative Turán density, denoted by , is the supremum over such that every ordered graph …
On the Turánability and tileability of oriented graphs
Igor Araujo, Zimu Xiang
An oriented graph is Turánable (resp. tileable) if there exist such that every semi-regular near-tournament on vertices contains a copy of …
Results and Problems on Equitable Coloring of Graphs
H. A. Kierstead, Alexandr Kostochka, Zimu Xiang
A proper coloring of vertices of a graph is equitable if the sizes of any two color classes differ by at most 1. Such colorings have many applications and are interesting by themse…