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Anti-Ramsey problems in the Mycielskian of a cycle

Author

Listed:
  • Hu, Wenjie
  • Li, Yibo
  • Liu, Huiqing
  • Hu, Xiaolan

Abstract

Let G and H be two graphs. The maximum integer k, for which there exists an edge coloring ϕ:E(G)→{1,2,…,k} that makes every copy of H has at least two edges with the same color, is the anti-Ramsey number of G with respect to H. Mycielski developed an interesting graph transformation that transforms G into the Mycielskian μ(G) of G. In this paper, we determine the anti-Ramsey number of μ(Cn) with respect to cycles of length 4, 2n and 2n+1, respectively.

Suggested Citation

  • Hu, Wenjie & Li, Yibo & Liu, Huiqing & Hu, Xiaolan, 2023. "Anti-Ramsey problems in the Mycielskian of a cycle," Applied Mathematics and Computation, Elsevier, vol. 459(C).
    • Handle: RePEc:eee:apmaco:v:459:y:2023:i:c:s0096300323004368
    DOI: 10.1016/j.amc.2023.128267
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    References listed on IDEAS

    as
    1. Pei, Yifan & Lan, Yongxin & He, Hua, 2022. "Improved bounds for anti-Ramsey numbers of matchings in outer-planar graphs," Applied Mathematics and Computation, Elsevier, vol. 418(C).
    2. Xu, Jiale & Lu, Mei & Liu, Ke, 2021. "Anti-Ramsey problems for cycles," Applied Mathematics and Computation, Elsevier, vol. 408(C).
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