IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v286y2016icp228-231.html
   My bibliography  Save this article

Odd components of co-trees and graph embeddings

Author

Listed:
  • Ren, Han
  • Chao, Fugang

Abstract

In this paper we investigate the relation between odd components of co-trees and graph embeddings. We show that any graph G must share one of the following two conditions: (a) for each integer h such that G may be embedded on Sh, the sphere with h handles, there is a spanning tree T in G such that h=12(β(G)−ω(T)), where β(G) and ω(T) are, respectively, the Betti number of G and the number of components of G−E(T) having odd number of edges; (b) for every spanning tree T of G, there is an orientable embedding of G with exact ω(T)+1 faces. This extends Xuong and Liu’s theorem [9,13] to some other (possible) genera. Infinitely many examples show that there are graphs which satisfy (a) but (b). Those make a correction of a result of Archdeacon [2, Theorem 1].

Suggested Citation

  • Ren, Han & Chao, Fugang, 2016. "Odd components of co-trees and graph embeddings," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 228-231.
    • Handle: RePEc:eee:apmaco:v:286:y:2016:i:c:p:228-231
    DOI: 10.1016/j.amc.2016.04.027
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300316302776
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2016.04.027?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.

    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:286:y:2016:i:c:p:228-231. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.