For two graphs T and H and for an integer n, let ex(n, T,H) denote the maximum possible number of copies of T in an H-free graph on n vertices. The study of this function when T = K2 is a single edgeâ€¦ (More)

Let G be a graph on n vertices and let k be a fixed positive integer. We denote by Gk-out(G) the probability space consisting of subgraphs of G where each vertex v âˆˆ V (G) randomly picks k neighborsâ€¦ (More)

When m2(H) > m2(Km) we prove that with high probability, depending on the value of p, either one can maintain almost all copies of Km, or it is asymptotically best to take a Ï‡(H) âˆ’ 1 partite subgraphâ€¦ (More)

For two fixed graphs T and H let ex(G(n, p), T,H) be the random variable counting the maximum number of copies of T in an H-free subgraph of the random graph G(n, p). We show that for the case T = Kmâ€¦ (More)

We study the following generalization of the TurÃ¡n problem in sparse random graphs. Given graphs T and H, let ex ( G(n, p), T,H ) be the random variable that counts the largest number of copies of Tâ€¦ (More)

For two graphs T and H with no isolated vertices and for an integer n, let ex(n, T,H) denote the maximum possible number of copies of T in an H-free graph on n vertices. The study of this functionâ€¦ (More)

We introduce and study a novel semi-random multigraph process, described as follows. The process starts with an empty graph on n vertices. In every round of the process, one vertex v of the graph isâ€¦ (More)

Let N be a finite set, let p âˆˆ (0, 1), and let Np denote a random binomial subset of N where every element of N is taken to belong to the subset independently with probability p. This defines aâ€¦ (More)

In [Tal94], Talagrand showed a generalization of the celebrated KKL theorem. In this work, we prove that the converse of this generalization also holds. Namely, for any sequence of numbers 0 < a1,â€¦ (More)