Textbook in PDF format

Combinatorics belongs to those areas of mathematics having experienced a most impressive growth in recent years. This growth has been fuelled in large part by the increasing importance of computers, the needs of computer science and demands from applications where discrete models play more and more important roles. But also more classical branches of mathematics have come to recognize that combinatorial structures are essential components of many mathematical theories.
Despite the dynamic state of this development, we feel that the time is ripe for summarizing the current status of the field and for surveying those major results that in our opinion will be of long-term importance. We approached leading experts in all areas of combinatorics to write chapters for this Handbook. The response was overwhelmingly enthusiastic and the result is what you see here.
The intention of the Handbook is to provide the working mathematician or computer scientist with a good overview of basic methods and paradigms, as well as important results and current issues and trends across the broad spectrum of com- combinatorics. However, our hope is that even specialists can benefit from reading this Handbook, by learning a leading expert's coherent and individual view of the topic.
As the reader will notice by looking at the table of contents, we have structured the Handbook into five sections: Structures, Aspects, Methods, Applications, and Horizons. We feel that viewing the whole field from different perspectives and taking different cross-sections will help to understand the underlying framework of the subject and to see the interrelationships more clearly. As a consequence of this approach, a number of the fundamental results occur in more than one chap- chapter. We believe that this is an asset rather than a shortcoming, since it illustrates different viewpoints and interpretations of the" results.
We thank the authors not only for writing the chapters but also for many helpful suggestions on the organization of the book and the presentation of the material. Many colleagues have contributed to the Handbook by reading the initial versions of the chapters and by making proposals with respect to the inclusion of topics and results as well as the structuring of the chapters. We are grateful for the significant help we received.
Even though this Handbook is quite voluminous, it was inevitable that some areas of combinatorics had to be left out or were not covered in the depth they deserved. Nevertheless, we believe that the Handbook of Combinatorics presents a comprehensive and accessible view of the present state of the field and that it will prove to be of lasting value.
Volume I
Structures
Graphs
Basic Graph Theory: Paths and Circuits
Connectivity and Network Flows
Matchings and Extensions
Colouring, Stable Sets and Perfect Graphs
Appendix to Chapter 4: Nowhere-Zero Flows
Embeddings and Minors
Random Graphs
Finite Sets and Relations
Hypergraphs
Partially Ordered Sets
Matroids
Matroids: Fundamental Concepts
Matroid Minors
Matroid Optimization and Algorithms
Symmetric Structures
Permutation Groups
Finite Geometries
Block Designs
Association Schemes
Codes
Combinatorial Structures in Geometry and Number Theory
Extremal Problems in Combinatorial Geometry
Convex Polytopes and Related Complexes
Point Lattices
Combinatorial Number Theory