Bounded quantifier depth spectra for random graphs

Joel Spencer, M. E. Zhukovskii

Research output: Contribution to journalArticle

Abstract

For which α there are first order graph statements A of given quantifier depth k such that a Zero-One law does not hold for the random graph G(n,p(n)) with p(n) at or near (there are two notions) n? A fairly complete description is given in both the near dense (α near zero) and near linear (α near one) cases.

Original languageEnglish (US)
Pages (from-to)1651-1664
Number of pages14
JournalDiscrete Mathematics
Volume339
Issue number6
DOIs
StatePublished - Jun 6 2016

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Quantifiers
Random Graphs
Zero-one Law
First-order
Zero
Graph in graph theory

Keywords

  • First-order logic
  • Random graphs
  • Spectra
  • Zero-one laws

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Bounded quantifier depth spectra for random graphs. / Spencer, Joel; Zhukovskii, M. E.

In: Discrete Mathematics, Vol. 339, No. 6, 06.06.2016, p. 1651-1664.

Research output: Contribution to journalArticle

Spencer, Joel ; Zhukovskii, M. E. / Bounded quantifier depth spectra for random graphs. In: Discrete Mathematics. 2016 ; Vol. 339, No. 6. pp. 1651-1664.
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