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Extremal coloring for the anti-Ramsey problem of matchings in complete graphs

Author

Listed:
  • Zemin Jin

    (Zhejiang Normal University)

  • Yuefang Sun

    (Shaoxing University)

  • Sherry H. F. Yan

    (Zhejiang Normal University)

  • Yuping Zang

    (Zhejiang Normal University)

Abstract

Given a graph G, the anti-Ramsey number $$AR(K_n,G)$$ A R ( K n , G ) is defined to be the maximum number of colors in an edge-coloring of $$K_n$$ K n which does not contain any rainbow G (i.e., all the edges of G have distinct colors). The anti-Ramsey number was introduced by Erdős et al. (Infinite and finite sets, pp 657–665, 1973) and so far it has been determined for several special graph classes. Another related interesting problem posed by Erdős et al. is the uniqueness of the extremal coloring for the anti-Ramsey number. Contrary to the anti-Ramsey number, there are few results about the extremal coloring. In this paper, we show the uniqueness of such extremal coloring for the anti-Ramsey number of matchings in the complete graph.

Suggested Citation

  • Zemin Jin & Yuefang Sun & Sherry H. F. Yan & Yuping Zang, 2017. "Extremal coloring for the anti-Ramsey problem of matchings in complete graphs," Journal of Combinatorial Optimization, Springer, vol. 34(4), pages 1012-1028, November.
    • Handle: RePEc:spr:jcomop:v:34:y:2017:i:4:d:10.1007_s10878-017-0125-1
    DOI: 10.1007/s10878-017-0125-1
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    References listed on IDEAS

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    1. Zemin Jin & Yuping Zang, 2017. "Anti-Ramsey coloring for matchings in complete bipartite graphs," Journal of Combinatorial Optimization, Springer, vol. 33(1), pages 1-12, January.
    2. Jin, Zemin, 2017. "Anti-Ramsey numbers for matchings in 3-regular bipartite graphs," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 114-119.
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    Cited by:

    1. Liu, Huiqing & Lu, Mei & Zhang, Shunzhe, 2022. "Anti-Ramsey numbers for cycles in the generalized Petersen graphs," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    2. Qin, Zhongmei & Li, Shasha & Lan, Yongxin & Yue, Jun, 2021. "Rainbow numbers for paths in planar graphs," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    3. Jin, Zemin & Jie, Qing & Cao, Zhenxin, 2024. "Rainbow disjoint union of P4 and a matching in complete graphs," Applied Mathematics and Computation, Elsevier, vol. 474(C).
    4. Jin, Zemin & Ma, Huawei & Yu, Rui, 2022. "Rainbow matchings in an edge-colored planar bipartite graph," Applied Mathematics and Computation, Elsevier, vol. 432(C).

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    1. Jin, Zemin & Ma, Huawei & Yu, Rui, 2022. "Rainbow matchings in an edge-colored planar bipartite graph," Applied Mathematics and Computation, Elsevier, vol. 432(C).
    2. Liu, Huiqing & Lu, Mei & Zhang, Shunzhe, 2022. "Anti-Ramsey numbers for cycles in the generalized Petersen graphs," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    3. Jin, Zemin & Jie, Qing & Cao, Zhenxin, 2024. "Rainbow disjoint union of P4 and a matching in complete graphs," Applied Mathematics and Computation, Elsevier, vol. 474(C).
    4. 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).

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