Erdos-Stone Theorem

The Erdos-Stone Theorem gives the asymptotic maximum number of edges a graph on n vertices can have while still avoiding a fixed forbidden subgraph, expressing that maximum as a fraction of the total possible edges determined by the forbidden subgraph's chromatic number, plus a smaller error term that vanishes as n grows. Named for Paul Erdos and Arthur Stone, it is the central asymptotic result of extremal graph theory, extending the earlier Turan's Theorem, which addresses only the special case of forbidding a complete graph.