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Mat. Sb., 2016, Volume 207, Number 3, Pages 153–174 (Mi msb8411)  

This article is cited in 1 scientific paper (total in 1 paper)

Zero-one law for random subgraphs of some distance graphs with vertices in $\mathbb Z^n$

S. N. Popova

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The zero-one law for the model of random distance graphs with vertices in $\mathbb Z^n$ is studied. Sufficient conditions for a sequence of random distance graphs to obey the zero-one law are derived, as well as conditions under which it contains a subsequence obeying the zero-one law.
Bibliography: 20 titles.

Keywords: random graphs, zero-one law, distance graphs.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation МК-2184.2014.1
This work was supported by the Council of the President of the Russian Federation for the Support of Young Russian Candidates of Science (grant no. MK-2184.2014.1).


DOI: https://doi.org/10.4213/sm8411

Full text: PDF file (625 kB)
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English version:
Sbornik: Mathematics, 2016, 207:3, 458–478

Bibliographic databases:

UDC: 519.179.4
MSC: 05C80, 60F20
Received: 28.07.2014 and 13.07.2015

Citation: S. N. Popova, “Zero-one law for random subgraphs of some distance graphs with vertices in $\mathbb Z^n$”, Mat. Sb., 207:3 (2016), 153–174; Sb. Math., 207:3 (2016), 458–478

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/msb/v207/i3/p153

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. E. Zhukovskii, A. M. Raigorodskii, “Random graphs: models and asymptotic characteristics”, Russian Math. Surveys, 70:1 (2015), 33–81  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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