Clara Shikhelman, Tel-Aviv University

Abstract

For two fixed graphs $T$ and $H$, a positive integer $n$ and a real number $p in [0,1]$ 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 $G(n,p)$. In this talk we discuss this variable, its phase transition as a function of $p$ and its connection to the deterministic function counting the maximum number of copies of $T$ in an $H$-free graph on $n$ vertices. Based on joint works with N. Alon, A. Kostochka and W. Samotij.