IDEAS home Printed from https://ideas.repec.org/p/crg/wpaper/dt2013-13.html
   My bibliography  Save this paper

On suficient conditions involving distances for hamiltonian properties in graphs

Author

Listed:
  • Ahmed Ainouche

    (UAG - CEREGMIA,Campus de Schoelcher B.P. 7209, 97275 Schoelcher Cedex Martinique (FRANCE))

Abstract

Let G be a 2-connected graph of order A set is essential if it is independent and contains two vertices at distance two apart. For = f 1 2 3g we de…ne min max to be respectively the smallest, the second smallest and the largest value in f 12 23 31g where = j ( ) \ ( )j In this paper we show that the closure concept can be used to prove su¢cient conditions on hamiltonicity when distances are involved. As main results, we prove for instance that if either (i) each essential triple of satis…es the condition 2 ( ) ¸ + or (ii) j ( ) [ ( )j + min f ( ) ( )g ¸ for all pairs of ( ) at distance two then its 0-dual closure is complete. By allowing classes of nonhamiltonian graphs we extend this result by one unit. A large number of new su¢cient conditions are derived. The proofs are short and all the results are sharp. Key words: Hamiltonian graph, closure, dual closure, neighborhood closure, essential sets.

Suggested Citation

  • Ahmed Ainouche, 2013. "On suficient conditions involving distances for hamiltonian properties in graphs," Documents de Travail 2013-13, CEREGMIA, Université des Antilles et de la Guyane.
  • Handle: RePEc:crg:wpaper:dt2013-13
    as

    Download full text from publisher

    File URL: http://www2.univ-ag.fr/RePEc/DT/DT2013-13_Ainouche.pdf
    File Function: First version, 2013
    Download Restriction: no
    ---><---

    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:crg:wpaper:dt2013-13. 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: Janis Hilaricus (email available below). General contact details of provider: https://edirc.repec.org/data/ceuagmq.html .

    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.