chapter  12
Extremal Graph Theory
Pages 30

In this final chapter, we introduce an area of graph theory referred to as extremal graph theory. Of the many problems encountered in this area, a common one asks for the minimum size of a graph G of a given order which guarantees that G contains a certain subgraph or possesses a certain property. While a result of this type due to Paul Tura´n is often considered the beginning of extremal graph theory, there is a host of problems that may be considered as belonging to this area, including problems dealing with the existence of regular graphs of a given degree and a given girth as well as several that lie in a well-known area of graph theory called Ramsey theory.