Written by international experts in the field of integer programming, this text and reference presents the mathematical foundations, theory, and algorithms of discrete optimization methods, incorporating many techniques as well as numerous examples and model formulations. Throughout, the notation used is clear and consistent and the level of mathematics never becomes excessive: difficult theorems are approached via a series of propositions, and proofs accurately reference the earlier results at each stage.

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...

A complete, highly accessible introduction to one of today’ s most exciting areas of applied mathematics One of the youngest, most vital areas of applied mathematics, combinatorial optimization integrates techniques from combinatorics, linear programming, and the theory of algorithms. Because of its success in solving difficult problems in areas from telecommunications to VLSI, from product distribution to airline crew scheduling, the field has seen a ground swell of activity over the past decade. Combinatorial Optimization is an ideal introduction to this mathematical discipline for...

The probabalistic method, allows us to prove the existence of combinatorial structure with certain properties by constructing an appropriate probability space and showing that a chosen element has the desired properties with positive probability.