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Mat. Tr., 2016, Volume 19, Number 1, Pages 106–177 (Mi mt302)  
Zero-one laws for random graphs with vertices in a Boolean cube

S. N. Popova

Lomonosov Moscow State University, Moscow, Russia

Abstract: We study the limit probabilities of first-order properties for random graphs with vertices in a Boolean cube. We find sufficient conditions for a sequence of random graphs to obey the zero-one law for first-order formulas of bounded quantifier depth. We also find conditions implying a weakened version of the zero-one law.

Key words: random graphs, zero-one laws, distance graphs.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation МК-2184.2014.1


DOI: https://doi.org/10.17377/mattrudy.2016.19.105

Full text: PDF file (575 kB)
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English version:
Siberian Advances in Mathematics, 2017, 27:1, 26–75

Bibliographic databases:

UDC: 519.175.4
Received: 17.11.2014

Citation: S. N. Popova, “Zero-one laws for random graphs with vertices in a Boolean cube”, Mat. Tr., 19:1 (2016), 106–177; Siberian Adv. Math., 27:1 (2017), 26–75

Citation in format AMSBIB
\Bibitem{Pop16}
\by S.~N.~Popova
\paper Zero-one laws for random graphs with vertices in a Boolean cube
\jour Mat. Tr.
\yr 2016
\vol 19
\issue 1
\pages 106--177
\mathnet{http://mi.mathnet.ru/mt302}
\crossref{https://doi.org/10.17377/mattrudy.2016.19.105}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3588301}
\elib{https://elibrary.ru/item.asp?id=25963587}
\transl
\jour Siberian Adv. Math.
\yr 2017
\vol 27
\issue 1
\pages 26--75
\crossref{https://doi.org/10.3103/S1055134417010035}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85014057607}


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