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Anti-Ramsey numbers for cycles in the generalized Petersen graphs

Author

Listed:
  • Liu, Huiqing
  • Lu, Mei
  • Zhang, Shunzhe

Abstract

For H⊆G, the anti-Ramsey number ar(G,H) is the maximum number of colors in an edge-coloring of G such that each subgraph isomorphic to H has at least two edges in the same color. The study of anti-Ramsey number ar(Kn,H) was introduced by Erdős et al. in 1973, and plentiful results were researched for some special graph H. Later, the problem was extended to ar(G,H) when replacing Kn by other graph G such as hypergraph, complete split graph, regular bipartite graph, triangulation and so on. In this paper, we consider a generalized Petersen graph Pn,k as the host graph and determine the exact anti-Ramsey numbers for cycles C5 and C6 in Pn,k, respectively.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:430:y:2022:i:c:s0096300322003514
    DOI: 10.1016/j.amc.2022.127277
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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. 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, 2017. "Anti-Ramsey numbers for matchings in 3-regular bipartite graphs," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 114-119.
    4. Xu, Jiale & Lu, Mei & Liu, Ke, 2021. "Anti-Ramsey problems for cycles," Applied Mathematics and Computation, Elsevier, vol. 408(C).
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