Nullspace embeddings for outerplanar graphs

László Lovász, Alexander Schrijver

Research output: Chapter in Book/Report/Conference proceedingChapter

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.

Original languageEnglish
Title of host publicationA Journey through Discrete Mathematics
Subtitle of host publicationA Tribute to Jiri Matousek
PublisherSpringer International Publishing
Pages571-591
Number of pages21
ISBN (Electronic)9783319444796
ISBN (Print)9783319444789
DOIs
Publication statusPublished - Jan 1 2017

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ASJC Scopus subject areas

  • Computer Science(all)
  • Mathematics(all)
  • Economics, Econometrics and Finance(all)
  • Business, Management and Accounting(all)

Cite this

Lovász, L., & Schrijver, A. (2017). Nullspace embeddings for outerplanar graphs. In A Journey through Discrete Mathematics: A Tribute to Jiri Matousek (pp. 571-591). Springer International Publishing. https://doi.org/10.1007/978-3-319-44479-6_23