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Anti-Ramsey coloring for matchings in complete bipartite graphs

Author

Listed:
  • Zemin Jin

    (Zhejiang Normal University)

  • Yuping Zang

    (Zhejiang Normal University)

Abstract

The anti-Ramsey number AR(G, H) is defined to be the maximum number of colors in an edge coloring of G which doesn’t contain any rainbow subgraphs isomorphic to H. It is clear that there is an $$AR(K_{m,n},kK_2)$$ A R ( K m , n , k K 2 ) -edge-coloring of $$K_{m,n}$$ K m , n that doesn’t contain any rainbow $$kK_2$$ k K 2 . In this paper, we show the uniqueness of this kind of $$AR(K_{m,n},kK_2)$$ A R ( K m , n , k K 2 ) -edge-coloring of $$K_{m,n}$$ K m , n .

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:33:y:2017:i:1:d:10.1007_s10878-015-9926-2
    DOI: 10.1007/s10878-015-9926-2
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    Citations

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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. 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.
    3. Jin, Zemin & Ma, Huawei & Yu, Rui, 2022. "Rainbow matchings in an edge-colored planar bipartite graph," Applied Mathematics and Computation, Elsevier, vol. 432(C).
    4. 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).

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