steinitz representations of polyhedra and the colin de verdière number

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22 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 1 2001

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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