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 …

В настоящей статье представлен обзор известных результатов в области предельного
поведения вероятностей свойств первого порядка случайных графов. Совокупность …

In this paper, we overview three closely related problems: Nelson–Hadwiger problem on
coloring spaces with forbidden monochromatics distances; Borsuk's problem on partitioning …

The paper deals with estimating the r-colorability threshold for a random k-uniform
hypergraph in the binomial model H (n, k, p). We consider the sparse case, when the …

Given positive integers $ n\ge 2k $, the {\it Kneser graph} $ KG_ {n, k} $ is a graph whose
vertex set is the collection of all $ k $-element subsets of the set $\{1,\ldots, n\} $, with edges …

The Kneser graph $ KG_ {n, k} $ is the graph whose vertices are the $ k $-element subsets
of $[n], $ with two vertices adjacent if and only if the corresponding sets are disjoint. A …

Graphs which are analogs of Kneser graphs are studied. The problem of determining the
chromatic numbers of these graphs is considered. It is shown that their structure is similar to …

We study the chromatic number of the graph G (n, 3, 1), whose vertices are all 3-element
subsets of [n]={1, 2,…, n}, and there is an edge between two vertices if the corresponding …

A new statement of a recent theorem of [1, 2] on the maximum number of edges in a
hypergraph with forbidden cardinalities of edge intersections is given. This statement is …

On the Stability of the Independence Number of a Random Subgraph Page 1 628 ISSN
1064-5624, Doklady Mathematics, 2017, Vol. 96, No. 3, pp. 628–630. © Pleiades Publishing …