Nullspace embeddings for outerplanar graphs

László Lovász, Alexander Schrijver

Research output: Chapter in Book/Report/Conference proceedingChapter


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
Number of pages21
ISBN (Electronic)9783319444796
ISBN (Print)9783319444789
Publication statusPublished - Jan 1 2017


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.