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Mat. Sb., 2018, Volume 209, Number 2, Pages 22–46 (Mi msb8674)  

Small subgraphs and their extensions in a random distance graph

A. V. Burkina, M. E. Zhukovskiibc

a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Department of Innovations and High Technology, Moscow Institute of Physics and Technology
c Peoples Friendship University of Russia, Moscow

Abstract: Some statements related to the distribution of small subgraphs in a sequence of random distance graphs are established. A result on the threshold function for the property of containing a fixed strictly balanced graph was proved before, and stronger generalizations of this result are obtained here.
Bibliography: 21 titles.

Keywords: distance graph, small subgraphs, extension properties, threshold function, random graph.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-03530-а
16-31-60052 мол_а_дк
Ministry of Education and Science of the Russian Federation 02.А03.21.0008
This research was carried out with the support of the Russian Foundation for Basic Research (grant nos. 15-01-03530-a and 16-31-60052 мол_а_дк) and the Ministry of Education and Science of the Russian Federation (agreement no. 02.A03.21.0008).

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm8674

Full text: PDF file (778 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2018, 209:2, 163–186

Bibliographic databases:

UDC: 519.179.4
MSC: Primary 05C12, 05C80; Secondary 60C05
Received: 15.02.2016 and 23.12.2016

Citation: A. V. Burkin, M. E. Zhukovskii, “Small subgraphs and their extensions in a random distance graph”, Mat. Sb., 209:2 (2018), 22–46; Sb. Math., 209:2 (2018), 163–186

Citation in format AMSBIB
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