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Generalized List Colouring of Graphs

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Abstract

This paper disproves a conjecture in Wang et al. (Graphs Comb. 31:1779–1787, 2015) and answers in the negative a question in Dvořák et al. (Electron J Comb:P26, 2019). In return, we pose five open problems.

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References

  1. Dvořák, Z., Pekárek, J., Sereni, J.: On generalized choice and coloring numbers. Electron. J. Comb. P26 (2019)

  2. Wang, W., Wu, B., Yan, Z., Xie, N.: A weaker version of a conjecture on list vertex arboricity of graphs. Graphs Comb. 31, 1779–1787 (2015)

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  3. Zhen, L., Wu, B.: List point arboricity of dense graphs. Graphs Comb. 25, 123–128 (2009)

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Funding

Supported by the Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education (No. NRF-2020R1I1A1A0105858711). Supported by the Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education (No. NRF-2018R1D1A1B07043049), and also by the Hankuk University of Foreign Studies Research Fund. Supported by the National Research Foundation of Korea grant funded by the Korea government (No. NRF-2021R1C1C1010763), and also by INHA UNIVERSITY Research Grant. Supported by the National Research Foundation of Korea grant funded by the Korea government (No. NRF-2018R1C1B6003577). Supported by NSFC 11971438, ZJNSF LD19A010001 and 111 project of the Ministry of Education of China.

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Authors and Affiliations

  1. Department of Mathematics, Hankuk University of Foreign Studies, Yongin, Gyeonggi, Republic of Korea

    Eun-Kyung Cho & Ilkyoo Choi

  2. Department of Mathematics, Zhejiang Normal University, Jinhua, China

    Yiting Jiang, Jiayan Yan & Xuding Zhu

  3. Department of Mathematics, Inha University, Incheon, Republic of Korea

    Ringi Kim

  4. Department of Mathematics, Ajou University, Suwon, Gyeonggi, Republic of Korea

    Boram Park

Authors
  1. Eun-Kyung Cho
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  2. Ilkyoo Choi
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  3. Yiting Jiang
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  4. Ringi Kim
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  5. Boram Park
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  6. Jiayan Yan
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  7. Xuding Zhu
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Corresponding author

Correspondence to Xuding Zhu.

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Cho, EK., Choi, I., Jiang, Y. et al. Generalized List Colouring of Graphs. Graphs and Combinatorics 37, 2121–2127 (2021). https://doi.org/10.1007/s00373-021-02336-3

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  • DOI: https://doi.org/10.1007/s00373-021-02336-3

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