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Alon–Tarsi Number and Modulo Alon–Tarsi Number of Signed Graphs

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Abstract

We extend the concept of the Alon–Tarsi number for unsigned graph to signed one. Moreover, we introduce the modulo Alon–Tarsi number for a prime number p. We show that both the Alon–Tarsi number and modulo Alon–Tarsi number of a signed planar graph \((G,\sigma )\) are at most 5, where the former result generalizes Zhu’s result for unsigned case and the latter one implies that \((G,\sigma )\) is \({\mathbb {Z}}_5\)-colorable.

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Acknowledgements

We would like to thank the anonymous referee for many helpful comments.

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Authors and Affiliations

  1. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, People’s Republic of China

    Wei Wang & Jianguo Qian

  2. College of Information Engineering, Tarim University, Alar, 843300, People’s Republic of China

    Wei Wang

  3. Graduate School of Environmental and Information Science, Yokohama National University, Yokohama, 240-8501, Japan

    Toshiki Abe

Authors
  1. Wei Wang
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  2. Jianguo Qian
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  3. Toshiki Abe
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Correspondence to Jianguo Qian.

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Supported by the National Natural Science Foundation of China under Grant nos. 11471273 and 11561058.

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Wang, W., Qian, J. & Abe, T. Alon–Tarsi Number and Modulo Alon–Tarsi Number of Signed Graphs. Graphs and Combinatorics 35, 1051–1064 (2019). https://doi.org/10.1007/s00373-019-02056-9

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  • DOI: https://doi.org/10.1007/s00373-019-02056-9

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