Description
Abstract:
Let F and H be graphs. The subgraph counting function ex(n,H,F) is defined as the maximum possible number of subgraphs
H in an n-vertex F-free graph. This function is a direct generalization of the Turan function as ex(n,F)=ex(n,K_2,F).
The systematic study of ex(n,H,F) was initiated by Alon and Shikhelman in 2016 who generalized several classical results in extremal graph theory to the subgraph counting setting.
Prior to their paper, a number of individual cases were investigated; a well-known example is the question to determine the maximum number of pentagons in a triangle-free graph.
In this talk we will survey results on the function ex(n,H,F) including a number of recent papers. We will also discuss this function's connection to hypergraph Turan problems.