M. E. Zhukovskii, A. M. Raigorodskii, “Random graphs: models and asymptotic characteristics”, Uspekhi Mat. Nauk, 2015, Volume 70, Issue 1(421),Pages <nobr>35

This article is cited in 49 papers

Random graphs: models and asymptotic characteristics

M. E. Zhukovskii^a, A. M. Raigorodskii^ab

^a Moscow Institute of Physics and Technology (State University)
^b Moscow State University

Abstract: This is a survey of known results related to the asymptotic behaviour of the probabilities of first-order properties of random graphs. The results presented in this paper are concerned with zero-one laws for properties of random graphs. Emphasis is placed on the Erdős–Rényi model of a random graph. Also considered are some generalizations of this model motivated by various problems in the theory of coding and combinatorial geometry.
Bibliography: 65 titles.

Keywords: random graphs, distance graphs, limit theorems, zero-one laws, first-order properties.

UDC: 519.175.4

MSC: Primary 05C80, 60F20; Secondary 03C07

Received: 05.09.2014

DOI: 10.4213/rm9626