Alon-Tarsi number of signed planar graphs
Wei Wang, Jianguo Qian

TL;DR
This paper extends the understanding of the Alon-Tarsi number for signed planar graphs, establishing upper bounds and providing examples related to colorability and choosability.
Contribution
It generalizes Zhu's result to signed graphs, showing the Alon-Tarsi number is at most 5, and proves a tighter bound of 4 for 2-colorable signed planar graphs.
Findings
Alon-Tarsi number of any signed planar graph is at most 5.
2-colorable signed planar graphs have Alon-Tarsi number at most 4.
Existence of 2-colorable signed planar graph not 3-choosable.
Abstract
Let be any signed planar graph. We show that the Alon-Tarsi number of is at most 5, generalizing a recent result of Zhu for unsigned case. In addition, if is -colorable then has the Alon-Tarsi number at most 4. We also construct a signed planar graph which is -colorable but not -choosable.
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Taxonomy
TopicsGraph Labeling and Dimension Problems · Advanced Graph Theory Research · Limits and Structures in Graph Theory
