Alon-Tarsi number of signed planar graphs

Wei Wang; Jianguo Qian

Alon-Tarsi number of signed planar graphs

Combinatorics 2018-09-11 v1

Authors: Wei Wang , Jianguo Qian

Abstract

Let $(G,\sigma)$ be any signed planar graph. We show that the Alon-Tarsi number of $(G,\sigma)$ is at most 5, generalizing a recent result of Zhu for unsigned case. In addition, if $(G,\sigma)$ is $2$ -colorable then $(G,\sigma)$ has the Alon-Tarsi number at most 4. We also construct a signed planar graph which is $2$ -colorable but not $3$ -choosable.

Keywords

signed planar graphs alon-tarsi number choosability colorability

Cite

@article{arxiv.1809.02907,
  title  = {Alon-Tarsi number of signed planar graphs},
  author = {Wei Wang and Jianguo Qian},
  journal= {arXiv preprint arXiv:1809.02907},
  year   = {2018}
}

Comments

14 pages,2 figures

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