IDEAS home Printed from https://ideas.repec.org/h/spr/oprchp/978-3-319-89920-6_26.html
   My bibliography  Save this book chapter

Closed Almost Knight’s Tours on 2D and 3D Chessboards

In: Operations Research Proceedings 2017

Author

Listed:
  • Michael Firstein

    (Alpen-Adria-Universität Klagenfurt)

  • Anja Fischer

    (Georg-August-Universität Göttingen)

  • Philipp Hungerländer

    (Alpen-Adria-Universität Klagenfurt)

Abstract

Let a (generalized) chessboard in two or three dimensions be given. A closed knight’s tour is defined as a Hamiltonian cycle over all cells of the chessboard where all moves are knight’s moves, i. e. have length $$\sqrt{5}$$ . It is well-characterized for which chessboard sizes it is not possible to construct a closed knight’s tour. On such chessboards a closed almost knight’s tour is defined as a Hamiltonian cycle of minimal length if only moves of length at least $$\sqrt{5}$$ are allowed. The problem of determining closed (almost) knight’s tours on 2D and 3D chessboards is equivalent to the so called traveling salesman problem with forbidden neighborhoods on regular 2D and 3D grids if the radius of the forbidden neighborhood is two and hence the minimal feasible distance of two consecutive vertices in the tour equals the length of a knight’s move. In this paper we present explicit construction schemes for closed almost knight’s tours by extending ideas used for the construction of knight’s tours.

Suggested Citation

  • Michael Firstein & Anja Fischer & Philipp Hungerländer, 2018. "Closed Almost Knight’s Tours on 2D and 3D Chessboards," Operations Research Proceedings, in: Natalia Kliewer & Jan Fabian Ehmke & Ralf Borndörfer (ed.), Operations Research Proceedings 2017, pages 185-190, Springer.
    • Handle: RePEc:spr:oprchp:978-3-319-89920-6_26
    DOI: 10.1007/978-3-319-89920-6_26
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    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:oprchp:978-3-319-89920-6_26. 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.