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The Chromatic Number of Graphs with No Induced Subdivision of \(K_4\)

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Abstract

In 2012, Lévêque, Maffray and Trotignon conjectured that if a graph does not contain an induced subdivision of \(K_4\), then it is 4-colorable. Recently, Le showed that every such graph is 24-colorable. In this paper, we improve the upper bound to 8.

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References

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Georgia State University, Atlanta, GA, 30303, USA

    Guantao Chen

  2. Research Center of Nonlinear Science, School of Mathematics and Computer Science, Wuhan Textile University, Wuhan, 430073, People’s Republic of China

    Yuan Chen

  3. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, People’s Republic of China

    Qing Cui

  4. Faculty of Science, Jiangxi University of Science and Technology, Ganzhou, 341000, People’s Republic of China

    Xing Feng

  5. Center for Discrete Mathematics, Fuzhou University, Fuzhou, 350108, People’s Republic of China

    Qinghai Liu

Authors
  1. Guantao Chen
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  2. Yuan Chen
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  3. Qing Cui
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  4. Xing Feng
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  5. Qinghai Liu
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Corresponding author

Correspondence to Yuan Chen.

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G. Chen: partially supported by the NSF Grant DMS-1855716. Y. Chen: partially supported by the National Natural Science Foundation of China (no. 11526160) and the Science and Technology Innovation Project of Wuhan Textile University. Q. Cui: partially supported by the National Natural Science Foundation of China (no. 11501291). X. Feng: partially supported by the Foundation of Jiangxi Provincial Education Department of China (no. GJJ190490). Q. Liu: partially supported by the National Natural Science Foundation of China (no. 11871015)

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Chen, G., Chen, Y., Cui, Q. et al. The Chromatic Number of Graphs with No Induced Subdivision of \(K_4\). Graphs and Combinatorics 36, 719–728 (2020). https://doi.org/10.1007/s00373-020-02148-x

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  • DOI: https://doi.org/10.1007/s00373-020-02148-x

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