IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v40y2020i4d10.1007_s10878-020-00644-7.html
   My bibliography  Save this article

Some algorithmic results for finding compatible spanning circuits in edge-colored graphs

Author

Listed:
  • Zhiwei Guo

    (Northwestern Polytechnical University
    University of Twente)

  • Hajo Broersma

    (University of Twente)

  • Ruonan Li

    (Northwestern Polytechnical University
    Northwestern Polytechnical University)

  • Shenggui Zhang

    (Northwestern Polytechnical University
    Northwestern Polytechnical University)

Abstract

A compatible spanning circuit in a (not necessarily properly) edge-colored graph G is a closed trail containing all vertices of G in which any two consecutively traversed edges have distinct colors. Sufficient conditions for the existence of extremal compatible spanning circuits (i.e., compatible Hamilton cycles and Euler tours), and polynomial-time algorithms for finding compatible Euler tours have been considered in previous literature. More recently, sufficient conditions for the existence of more general compatible spanning circuits in specific edge-colored graphs have been established. In this paper, we consider the existence of (more general) compatible spanning circuits from an algorithmic perspective. We first show that determining whether an edge-colored connected graph contains a compatible spanning circuit is an NP-complete problem. Next, we describe two polynomial-time algorithms for finding compatible spanning circuits in edge-colored complete graphs. These results in some sense give partial support to a conjecture on the existence of compatible Hamilton cycles in edge-colored complete graphs due to Bollobás and Erdős from the 1970s.

Suggested Citation

  • Zhiwei Guo & Hajo Broersma & Ruonan Li & Shenggui Zhang, 2020. "Some algorithmic results for finding compatible spanning circuits in edge-colored graphs," Journal of Combinatorial Optimization, Springer, vol. 40(4), pages 1008-1019, November.
    • Handle: RePEc:spr:jcomop:v:40:y:2020:i:4:d:10.1007_s10878-020-00644-7
    DOI: 10.1007/s10878-020-00644-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-020-00644-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10878-020-00644-7?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.

    Citations

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


    Cited by:

    1. Yuhang Bai & Zhiwei Guo & Shenggui Zhang & Yandong Bai, 2023. "Linear amortized time enumeration algorithms for compatible Euler trails in edge-colored graphs," Journal of Combinatorial Optimization, Springer, vol. 45(2), pages 1-20, March.

    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:spr:jcomop:v:40:y:2020:i:4:d:10.1007_s10878-020-00644-7. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.