Geodesic
Gigantic Component in Random Distance Graphs of Special Form
Matematičeskie zametki, Tome 92 (2012) no. 3, pp. 463-480

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We consider the problem of threshold probability for the existence of a gigantic component in a certain series of random distance graphs. The results obtained generalize the classical Erdős–Rényi theorems in the case of geometric graphs of special form.
Keywords: random distance graph, gigantic component in a random graph, classical Erdős–Rényi theorems, $k$-vertex tree, Stirling's formula. 
@article{MZM_2012_92_3_a14,
     author = {A. R. Yarmuhametov},
     title = {Gigantic {Component} in {Random} {Distance} {Graphs} of {Special} {Form}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {463--480},
     publisher = {mathdoc},
     volume = {92},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_92_3_a14/}
}
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A. R. Yarmuhametov. Gigantic Component in Random Distance Graphs of Special Form. Matematičeskie zametki, Tome 92 (2012) no. 3, pp. 463-480. http://geodesic.mathdoc.fr/item/MZM_2012_92_3_a14/