Geodesic
On embedding random graphs into distance graphs and graphs of diameters in Euclidean spaces
Čebyševskij sbornik, Tome 16 (2015) no. 2, pp. 133-143

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In this paper we consider the problem of finding the probability threshold for the realization of a random graph by geometric graphs in the space ${\mathbb R}^d$. In the case of graphs of diameters we prove asymptotic behavior for the threshold probability on the plane, as well as the exact expression in the case $d \ge 3$. Bibliography: 18 titles.
Keywords: distance graph, diameter graph, random graph. 
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     author = {A. V. Krot and A. M. Raigorodskii},
     title = {On embedding random graphs into distance graphs and graphs of diameters in {Euclidean} spaces},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {133--143},
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     year = {2015},
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A. V. Krot; A. M. Raigorodskii. On embedding random graphs into distance graphs and graphs of diameters in Euclidean spaces. Čebyševskij sbornik, Tome 16 (2015) no. 2, pp. 133-143. http://geodesic.mathdoc.fr/item/CHEB_2015_16_2_a8/