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Improved bounds for anti-Ramsey numbers of matchings in outer-planar graphs

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  • Pei, Yifan
  • Lan, Yongxin
  • He, Hua

Abstract

Let On be the set of all maximal outer-planar graphs of order n. Let ar(On,F) denote the maximum positive integer k such that there is a k-edge-coloring of a graph T in the family On which has no rainbow subgraph F. Denote by Mk a matching of size k. In this paper, we prove that ar(On,Mk)≤n+4k−9 for n≥3k−3, which expressively improves the existing upper bound for ar(On,Mk). We also prove that ar(On,M5)=n+4 for all n≥15.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:418:y:2022:i:c:s0096300321009267
    DOI: 10.1016/j.amc.2021.126843
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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.
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    Cited by:

    1. 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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