IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-319-44479-6_23.html
   My bibliography  Save this book chapter

Nullspace Embeddings for Outerplanar Graphs

In: A Journey Through Discrete Mathematics

Author

Listed:
  • László Lovász

    (Eötvös Loránd University)

  • Alexander Schrijver

    (University of Amsterdam and CWI)

Abstract

We study relations between geometric embeddings of graphs and the spectrum of associated matrices, focusing on outerplanar embeddings of graphs. For a simple connected graph G = (V, E), we define a “good” G-matrix as a V × V matrix with negative entries corresponding to adjacent nodes, zero entries corresponding to distinct nonadjacent nodes, and exactly one negative eigenvalue. We give an algorithmic proof of the fact that if G is a 2-connected graph, then either the nullspace representation defined by any “good” G-matrix with corank 2 is an outerplanar embedding of G, or else there exists a “good” G-matrix with corank 3.

Suggested Citation

  • László Lovász & Alexander Schrijver, 2017. "Nullspace Embeddings for Outerplanar Graphs," Springer Books, in: Martin Loebl & Jaroslav Nešetřil & Robin Thomas (ed.), A Journey Through Discrete Mathematics, pages 571-591, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-44479-6_23
    DOI: 10.1007/978-3-319-44479-6_23
    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
    for a similarly titled item that would be available.

    More about this item

    Statistics

    Access and download statistics

    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:sprchp:978-3-319-44479-6_23. 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.