The Alon-Tarsi number of planar graphs
Xuding Zhu
TL;DR
This paper proves that all planar graphs have an Alon-Tarsi number of at most 5, providing an alternative proof for their 5-choosability and 5-paintability properties.
Contribution
The paper establishes a new upper bound of 5 for the Alon-Tarsi number of planar graphs, offering an alternative proof for their 5-choosability and 5-paintability.
Findings
Alon-Tarsi number of planar graphs ≤ 5
Planar graphs are 5-choosable
Planar graphs are 5-paintable
Abstract
This paper proves that the Alon-Tarsi number of any planar graph is at most , which gives an alternate proof of the -choosability as well as the -paintability of planar graphs.
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
TopicsAdvanced Graph Theory Research · Computational Geometry and Mesh Generation · Optimization and Search Problems