IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v397y2021ics0096300320308717.html
   My bibliography  Save this article

Rainbow numbers for paths in planar graphs

Author

Listed:
  • Qin, Zhongmei
  • Li, Shasha
  • Lan, Yongxin
  • Yue, Jun

Abstract

Given a family of graphs F and a subgraph H of F∈F, let rb(F,H) denote the smallest number k so that there is a rainbow H in any k-edge-colored F. We call it rainbow number for H in regard to F. The set of all plane triangulations of order n is denoted by Tn. The wheel graph of order d+1 and the path of order k are denoted by Wd and Pk, respectively. In this paper, we establish lower bounds of rb(Tn,Pk) for all k≥8, which improves the results in [Y. Lan, Y. Shi and Z-X. Song, Planar anti-Ramsey numbers for paths and cycles, Discrete Math. 342(11) (2019), 3216–3224.]. In addition, we also attain the accurate values or bounds of rb(Tn,Pk) for 4≤k≤7. Furthermore, we get lower and upper bounds of rb(Wd,Pk) for all k≥9 and obtain the accurate values of rb(Wd,Pk) for k∈{4,5,6,7,8,d+1}.

Suggested Citation

  • Qin, Zhongmei & Li, Shasha & Lan, Yongxin & Yue, Jun, 2021. "Rainbow numbers for paths in planar graphs," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    • Handle: RePEc:eee:apmaco:v:397:y:2021:i:c:s0096300320308717
    DOI: 10.1016/j.amc.2020.125918
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300320308717
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2020.125918?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Qin, Zhongmei & Lei, Hui & Li, Shasha, 2020. "Rainbow numbers for small graphs in planar graphs," Applied Mathematics and Computation, Elsevier, vol. 371(C).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ahmed Badawy & Jesus A. Fisteus & Tarek M. Mahmoud & Tarek Abd El-Hafeez, 2021. "Topic Extraction and Interactive Knowledge Graphs for Learning Resources," Sustainability, MDPI, vol. 14(1), pages 1-21, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jin, Zemin & Ma, Huawei & Yu, Rui, 2022. "Rainbow matchings in an edge-colored planar bipartite graph," Applied Mathematics and Computation, Elsevier, vol. 432(C).
    2. 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).
    3. 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).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:397:y:2021:i:c:s0096300320308717. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.