IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v441y2023ics0096300322007603.html
   My bibliography  Save this article

On linear 2-arboricity of certain graphs

Author

Listed:
  • Chen, Jijuan
  • Wang, Tao

Abstract

The linear 2-arboricity of a graph G is the least number of forests which decomposes E(G) and each forest is a collection of paths of length at most two. A graph has property Pk, if each subgraph H satisfies one of the three conditions: (i) δ(H)≤1; (ii) there exists xy∈E(H) with degH(x)+degH(y)≤k; (iii) H contains a 2-alternating cycle. In this paper, we give two edge-decompositions of graphs with property Pk. Using these decompositions, we give an upper bound for the linear 2-arboricity in terms of Pk. We also prove that every plane graph with no 12+-vertex incident with a gem at the center has property P13, and graphs with maximum average degree less than 6k−6k+3 have property Pk, where k≥5 is an integer.

Suggested Citation

  • Chen, Jijuan & Wang, Tao, 2023. "On linear 2-arboricity of certain graphs," Applied Mathematics and Computation, Elsevier, vol. 441(C).
    • Handle: RePEc:eee:apmaco:v:441:y:2023:i:c:s0096300322007603
    DOI: 10.1016/j.amc.2022.127692
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300322007603
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2022.127692?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. Wang, Yiqiao & Wang, Weifan & Wang, Ying, 2018. "Edge-partition and star chromatic index," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 480-489.
    Full references (including those not matched with items on IDEAS)

    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. Cai, Jiansheng & Yang, Chunhua & Yu, Jiguo, 2019. "An upper bound for the choice number of star edge coloring of graphs," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 588-593.
    2. Holub, Přemysl & Lužar, Borut & Mihaliková, Erika & Mockovčiaková, Martina & Soták, Roman, 2021. "Star edge-coloring of square grids," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    3. Wang, Ying & Wang, Yiqiao & Wang, Weifan, 2019. "Star edge-coloring of graphs with maximum degree four," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 268-275.

    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:441:y:2023:i:c:s0096300322007603. 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.