Equitable list coloring of sparse graphs
H. A. Kierstead, Alexandr Kostochka, Zimu Xiang

TL;DR
This paper establishes sharp bounds for equitable list coloring of sparse graphs with minimum degree two, introducing the new concept of strongly equitable list coloring to achieve these results.
Contribution
It proves sharp bounds for equitable and equitable list coloring of specific sparse graphs, and introduces the new concept of strongly equitable list coloring.
Findings
Every (7/6,1/3)-sparse graph with minimum degree at least 2 is equitably 3-colorable and 3-choosable.
Every (5/4,1/2)-sparse graph with minimum degree at least 2 is equitably 4-colorable and 4-choosable.
The bounds are proven to be sharp.
Abstract
A proper vertex coloring of a graph is equitable if the sizes of all color classes differ by at most . For a list assignment of colors to each vertex of an -vertex graph , an equitable -coloring of is a proper coloring of vertices of from their lists such that no color is used more than times. Call a graph equitably -choosable if it has an equitable -coloring for every -list assignment . A graph is -sparse if for every , the number of edges in the subgraph of induced by is at most . Our first main result is that every -sparse graph with minimum degree at least is equitably -colorable and equitably -choosable. This is sharp. Our second main result is that every -sparse graph with minimum degree at least is…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGraph Labeling and Dimension Problems · Advanced Graph Theory Research
