Triangles in H-free graphs
For two graphs T and H and 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 = K_2 (a single edge) is one of the main subjects of extremal graph theory. We investigate the general function, focusing on the case T = K_3, which reveals several interesting phenomena.
The last statement improves (slightly) a result of Bollobas and Gyori.
Joint work with Noga Alon.