Erdős–Stone theorem

The Erdős–Stone theorem is a fundamental result in extremal graph theory, which deals with understanding the maximum number of edges in a graph that does not contain a particular subgraph. Specifically, the theorem provides a way to determine the asymptotic behavior of the maximum number of edges in a graph on \( n \) vertices that does not contain a complete subgraph \( K_r \) (the complete graph on \( r \) vertices) as a subgraph.