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Russian Mathematical Surveys, 2015, Volume 70, Issue 1, Pages 33–81
DOI: https://doi.org/10.1070/RM2015v070n01ABEH004936 (Mi rm9626) 		 
This article is cited in 47 scientific papers (total in 47 papers)

Random graphs: models and asymptotic characteristics

M. E. Zhukovskiia, A. M. Raigorodskiiab

a Moscow Institute of Physics and Technology (State University)
b Moscow State University
English version PDF (840 kB) Citations (47)
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DOI: https://doi.org/10.1070/RM2015v070n01ABEH004936
Abstract: This is a survey of known results related to the asymptotic behaviour of the probabilities of first-order properties of random graphs. The results presented in this paper are concerned with zero-one laws for properties of random graphs. Emphasis is placed on the Erdős–Rényi model of a random graph. Also considered are some generalizations of this model motivated by various problems in the theory of coding and combinatorial geometry.
Bibliography: 65 titles.
Keywords: random graphs, distance graphs, limit theorems, zero-one laws, first-order properties.
Funding agency Grant number
Russian Foundation for Basic Research 13-01-00612
15-01-00350
Ministry of Education and Science of the Russian Federation МД-6277.2013.1
МК-2184.2014.1
НШ-2519.2012.1
This work was supported by the Russian Foundation for Basic Research (projects nos. 13-01-00612 and 15-01-00350) and by the Council of the President of the Russian Federation for the Support of Young Russian Scientists and Leading Scientific Schools, grants МД-6277.2013.1, MK-2184.2014.1, and НШ-2519.2012.1.
Received: 05.09.2014
Russian version:
Uspekhi Matematicheskikh Nauk, 2015, Volume 70, Issue 1(421), Pages 35–88
DOI: https://doi.org/10.4213/rm9626
Bibliographic databases:
Document Type: Article
UDC: 519.175.4
MSC: Primary 05C80, 60F20; Secondary 03C07
Language: English
Original paper language: Russian
Citation: M. E. Zhukovskii, A. M. Raigorodskii, “Random graphs: models and asymptotic characteristics”, Uspekhi Mat. Nauk, 70:1(421) (2015), 35–88; Russian Math. Surveys, 70:1 (2015), 33–81
Citation in format AMSBIB
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    • This publication is cited in the following 47 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:92
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