Random Graphs

In 1959 P. Erdos and A. Renyi initiated the study of the binomial model of a random graph G(n,p), in which edges on n vertices are drawn independently, each with probability p. Now, the random graphs of Erdos and Renyi are among the most important subjects of combinatorics and its applications.
One natural generalization of the Erdos-Renyi model is as follows: given a sequence of graphs H_n we keep each of the edges of H_n with probability p independently of each others (no new edges are drawn). Thus appear random graphs H_{n,p}. In the last years, such models are being very intensively studied.
We will talk about one sequence of graphs, which is important for combinatorial geometry and coding theory. For this sequence of graphs, we will consider the above-described version of the Erdos-Renyi model. We will exhibit various old and new results. In particular, we will concentrate on colorings, cliques and independent sets.