This article is cited in 3 papers

Gigantic Component in Random Distance Graphs of Special Form

A. R. Yarmuhametov

M. V. Lomonosov Moscow State University

Abstract: 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.

UDC: 519.172

Received: 02.03.2011
Revised: 20.06.2011

DOI: 10.4213/mzm9066

 English version: Mathematical Notes, 2012, 92:3, 426–441

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