On the chromatic numbers of random graphs

In my talk, I suppose to speak about the chromatic numbers of random subgraphs in some graph sequences. First, I will present some classical results on the chromatic numbers of Erdős–Rényi graphs. Then, I will proceed to the discussion of new questions. For example, I will consider a sequence of graphs $G(n,r,s)$, where $n\to\infty $ and $r = r(n)$, $s = s(n)$. The set of vertices of $G(n,r,s)$ consists of all $r$ -subsets of the set $\{1, \dots, n\}$. Any two vertices are joined by an edge, if the corresponding sets intersect in exactly $s$ elements. Such graphs are related to coding theory, Ramsey theory and combinatorial geometry. I will define random subgraphs $G_{p}(n,r,s)$ of $G(n,r,s)$, where $p = p(n)\in [0,1]$ is the probability of keeping any edge in $G(n,r,s)$ independently of each other. I will discuss recent results concerning the chromatic numbers of such random graphs.