Bipartite Graphs and Their Applications

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Cambridge University Press, Jul 13, 1998 - Mathematics - 259 pages
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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.
 

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Contents

Basic concepts
1
Introduction to bipartite graphs
7
Metric properties
23
Connectivity
45
Maximum matchings
56
Expanding properties
75
Subgraphs with restricted degrees
97
Edge colourings
125
Doubly stochastic matrices and bipartite graphs
163
Coverings
174
Some combinatorial applications
192
Bipartite subgraphs of arbitrary graphs
214
Appendix
232
Index
256
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Page 243 - Ford, LR, and Fulkerson, DR, "Flows in Networks.
Page 240 - Some upper bounds on the total and list chromatic numbers of multigraphs, J. Graph Theory 16 (1992), 503-516.

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