Orthogonal representations and connectivity of graphs

L. Lovász, M. Saks, A. Schrijver

Research output: Contribution to journalArticle

47 Citations (Scopus)


It is proved that a graph on n nodes is k-connected if and only if its nodes can be represented by real vectors in dimension n - k such that (a) nonadjacent nodes are represented by orthogonal vectors and (b) any n - k of them are linearly independent. We show that the closure of the set of all representations with properties (a) and (b) is irreducible as an algebraic variety, and study the question of irreducibility of the variety of all representations with property (a).

Original languageEnglish
Pages (from-to)439-454
Number of pages16
JournalLinear Algebra and Its Applications
Issue numberC
Publication statusPublished - 1989

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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