Geodesic
Small subgraphs and their extensions in a~random distance graph
Sbornik. Mathematics, Tome 209 (2018) no. 2, pp. 163-186

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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. 
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A. V. Burkin; M. E. Zhukovskii. Small subgraphs and their extensions in a~random distance graph. Sbornik. Mathematics, Tome 209 (2018) no. 2, pp. 163-186. http://geodesic.mathdoc.fr/item/SM_2018_209_2_a1/