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Rainbow disjoint union of P4 and a matching in complete graphs

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  • Jin, Zemin
  • Jie, Qing
  • Cao, Zhenxin

Abstract

An edge-colored graph G is called rainbow if all the colors on its edges are distinct. Given graphs G and H, the anti-Ramsey number AR(G,H) is the maximum number k such that there exists an edge-coloring of G with exactly k colors containing no rainbow copy of H. Recently, the anti-Ramsey problem for disjoint union of graphs received much attention. In particular, several researchers focused on the problem for graphs consisting of small components. In this paper, we continue the work in this line. We refine the bound of n and determine the precise value of AR(Kn,P4∪tP2) for all n≥2t+4 in complete graphs.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:474:y:2024:i:c:s0096300324001516
    DOI: 10.1016/j.amc.2024.128679
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    References listed on IDEAS

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    1. Jin, Zemin, 2017. "Anti-Ramsey numbers for matchings in 3-regular bipartite graphs," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 114-119.
    2. 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.
    3. 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.
    Full references (including those not matched with items on IDEAS)

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