Bipartite Graphs and their Applications

This book treats the fundamental mathematical properties that hold for a family of Gaussian random variables.

Armen S. Asratian (Author), Tristan M. J. Denley (Author), Roland Häggkvist (Author)

9780521065122, Cambridge University Press

Paperback / softback, published 12 June 2008

272 pages
22.9 x 15 x 1.5 cm, 0.402 kg

"...the treatment of topics is clear and self-contained and shows considerable design, work, and thought...as a volume in the series Cambridge Tracts in Mathematics, this book has the mandate to 'take up a single thread in a wide subject and follow its ramifications, thus throwing light on its various aspects.' This book does that, beautifully." Siam Review

Bipartite graphs are perhaps the most basic of objects in graph theory, both from a theoretical and practical point of view. However, sometimes they have been considered only as a special class in some wider context. This book deals solely with bipartite graphs. Together with traditional material, the reader will also find many unusual results. Essentially all proofs are given in full; many of these have been streamlined specifically for this text. Numerous exercises of all standards have also been included. The theory is illustrated with many applications especially to problems in timetabling, chemistry, communication networks and computer science. For the most part the material is accessible to any reader with a graduate understanding of mathematics. However, the book contains advanced sections requiring much more specialized knowledge, which will be of interest to specialists in combinatorics and graph theory.

1. Basic concepts
2. Biparticity
3. Metric properties
4. Connectivity
5. Maximum matchings
6. Expanding properties
7. Subgraphs with restricted degrees
8. Edge colourings
9. Doubly stochastic matrices and bipartite graphs
10. Coverings
11. Some combinatorial applications
12. Bipartite subgraphs of arbitrary graphs.

Subject Areas: Combinatorics & graph theory [PBV]