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Anti-Ramsey problems for cycles

Author

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  • Xu, Jiale
  • Lu, Mei
  • Liu, Ke

Abstract

We call a subgraph of an edge-colored graph rainbow, if all of its edges have different colors. A rainbow copy of a graph H in an edge-colored graph G is a subgraph of G isomorphic to H such that the coloring restricted to this subgraph is a rainbow coloring. Given two graphs G and H, let Ar(G,H) denote the maximum number of colors in a coloring of the edges of G that has no any rainbow copy of H. When G is Kn, Ar(G,H) is called the anti-Ramsey number. Anti-Ramsey number was introduced by Erdös, Simonovits and Sós in the 1970s. Since then, the field has blossomed in a wide variety of papers and some other graphs were used as host graphs. In this paper, we give a new method to compute the anti-Ramsey number by constructing a corresponding hypergraph. As application, we determine the exact values of Ar(G,Ck) when the host graph G is Wd, Pm×Pn, Pm×Cn, Cm×Cn and cyclic Cayley graph, respectively.

Suggested Citation

  • Xu, Jiale & Lu, Mei & Liu, Ke, 2021. "Anti-Ramsey problems for cycles," Applied Mathematics and Computation, Elsevier, vol. 408(C).
    • Handle: RePEc:eee:apmaco:v:408:y:2021:i:c:s0096300321004343
    DOI: 10.1016/j.amc.2021.126345
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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. 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).

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