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.
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Taxonomy
TopicsAdvanced Graph Theory Research · Computational Geometry and Mesh Generation · Optimization and Search Problems
