### 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^{-α}? A fairly complete description is given in both the near dense (α near zero) and near linear (α near one) cases.

Original language | English (US) |
---|---|

Pages (from-to) | 1651-1664 |

Number of pages | 14 |

Journal | Discrete Mathematics |

Volume | 339 |

Issue number | 6 |

DOIs | |

State | Published - Jun 6 2016 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*339*(6), 1651-1664. https://doi.org/10.1016/j.disc.2016.01.005

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

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 339, no. 6, pp. 1651-1664. https://doi.org/10.1016/j.disc.2016.01.005

}

TY - JOUR

T1 - Bounded quantifier depth spectra for random graphs

AU - Spencer, Joel

AU - Zhukovskii, M. E.

PY - 2016/6/6

Y1 - 2016/6/6

N2 - 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-α? A fairly complete description is given in both the near dense (α near zero) and near linear (α near one) cases.

AB - 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-α? A fairly complete description is given in both the near dense (α near zero) and near linear (α near one) cases.

KW - First-order logic

KW - Random graphs

KW - Spectra

KW - Zero-one laws

UR - http://www.scopus.com/inward/record.url?scp=84958819011&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84958819011&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2016.01.005

DO - 10.1016/j.disc.2016.01.005

M3 - Article

VL - 339

SP - 1651

EP - 1664

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 6

ER -