IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v14y2007i1d10.1007_s10878-006-9034-4.html
   My bibliography  Save this article

Packing [1, Δ]-factors in graphs of small degree

Author

Listed:
  • Adrian Kosowski

    (Gdańsk University of Technology)

  • Michał Małafiejski

    (Gdańsk University of Technology)

  • Paweł Żyliński

    (University of Gdańsk)

Abstract

Given an undirected, connected graph G with maximum degree Δ, we introduce the concept of a [1, Δ]-factor k-packing in G, defined as a set of k edge-disjoint subgraphs of G such that every vertex of G has an incident edge in at least one subgraph. The problem of deciding whether a graph admits a [1,Δ]-factor k-packing is shown to be solvable in linear time for k = 2, but NP-complete for all k≥ 3. For k = 2, the optimisation problem of minimising the total number of edges of the subgraphs of the packing is NP-hard even when restricted to subcubic planar graphs, but can in general be approximated within a factor of $$\frac{42\Delta -30}{35\Delta-21}$$ by reduction to the Maximum 2-Edge-Colorable Subgraph problem. Finally, we discuss implications of the obtained results for the problem of fault-tolerant guarding of a grid, which provides the main motivation for research.

Suggested Citation

  • Adrian Kosowski & Michał Małafiejski & Paweł Żyliński, 2007. "Packing [1, Δ]-factors in graphs of small degree," Journal of Combinatorial Optimization, Springer, vol. 14(1), pages 63-86, July.
    • Handle: RePEc:spr:jcomop:v:14:y:2007:i:1:d:10.1007_s10878-006-9034-4
    DOI: 10.1007/s10878-006-9034-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-006-9034-4
    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/s10878-006-9034-4?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:spr:jcomop:v:14:y:2007:i:1:d:10.1007_s10878-006-9034-4. 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.