Extremal graphs and the Erdős-Stone-Simonovits theorems

Abstract

The Erdős-Stone-Simonovits theorems say that any graph F can be embedded in any graph G when G has a sufficient amount of vertices and edges. We will discuss some extremal problems and look at the Turán numbers of triangles, quadrilater- als and some other graphs leading up to the proof of the Erdős-Stone-Simonovits theorems.