Bipartite Graphs and Their Applications
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Bipartite graphs are perhaps the most basic of objects in graph theory, both from a theoretical and practical point of view. However, until now they have been considered only as a special class in some wider context. This is the first book which deals solely with bipartite graphs. Together with traditional material, the reader will also find many new and 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...
Bipartite graphs are perhaps the most basic of objects in graph theory, both from a theoretical and practical point of view. However, until now they have been considered only as a special class in some wider context. This is the first book which deals solely with bipartite graphs. Together with traditional material, the reader will also find many new and 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.
Table of contents:
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.
This is the first book which deals solely with bipartite graphs. 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 which will be of interest to specialists in combinatorics and graph theory.
This book treats the fundamental mathematical properties that hold for a family of Gaussian random variables.
Table of contents:
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.
This is the first book which deals solely with bipartite graphs. 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 which will be of interest to specialists in combinatorics and graph theory.
This book treats the fundamental mathematical properties that hold for a family of Gaussian random variables.
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