The theory of perfect graphs was born out of a conjecture about graph colouring made by Claude Berge in 1960. That conjecture remains unsolved, but has generated an important area of research in combinatorics. This book: Includes an introduction by Claude Berge, the founder of perfect graph theory Discusses the most recent developments in the field of perfect graph theory Provides a thorough historical overview of the subject Internationally respected authors highlight the new directions, seminal results and the links the field has with other subjects Discusses how semi-definite programming evolved out of perfect graph theory The early developments of the theory are included to lay the groundwork for the later chapters. The most recent developments of perfect graph theory are discussed in detail, highlighting seminal results, new directions, and links to other areas of mathematics and their applications. These applications include frequency assignment for telecommunication systems, integer programming and optimisation.