steinitz representations of polyhedra and the colin de verdière number

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

We show that the Steinitz representations of 3-connected planar graphs correspond, in a well described way, to Colin de Verdière matrices of such graphs. As an application, we prove a conjecture of Connelly on the eigenvalues of stress matrices of braced convex polytopes.

Original languageEnglish
Pages (from-to)223-236
Number of pages14
JournalJournal of Combinatorial Theory. Series B
Volume82
Issue number2
DOIs
Publication statusPublished - Jul 2001

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Polyhedron
Convex Polytopes
Planar graph
Connected graph
Eigenvalue
Graph in graph theory

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

steinitz representations of polyhedra and the colin de verdière number. / Lovász, L.

In: Journal of Combinatorial Theory. Series B, Vol. 82, No. 2, 07.2001, p. 223-236.

Research output: Contribution to journalArticle

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