Bipartite Graphs and their Applications

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Overview

Bipartite graphs are perhaps the most basic of objects in graph theory, both from a theoretical and from a 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. 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 specialised knowledge, which will be of interest to specialists in combinatorics and graph theory.
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Editorial Reviews

From the Publisher
"...excellent monograph...This is an invaluable book and an indispensable resource for any serious student of graph theory." Mathematics of Computing

"...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

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Product Details

  • ISBN-13: 9780521065122
  • Publisher: Cambridge University Press
  • Publication date: 6/12/2008
  • Series: Cambridge Tracts in Mathematics Series , #131
  • Edition description: Reissue
  • Pages: 272
  • Product dimensions: 6.00 (w) x 9.00 (h) x 0.80 (d)

Table of Contents

Preface
Notation
Ch. 1 Basic concepts 1
Ch. 2 Introduction to bipartite graphs 7
Ch. 3 Metric properties 23
Ch. 4 Connectivity 45
Ch. 5 Maximum matchings 56
Ch. 6 Expanding properties 75
Ch. 7 Subgraphs with restricted degrees 97
Ch. 8 Edge colourings 125
Ch. 9 Doubly stochastic matrices and bipartite graphs 163
Ch. 10 Coverings 174
Ch. 11 Some combinatorial applications 192
Ch. 12 Bipartite subgraphs of arbitrary graphs 214
Appendix 232
References 237
Index 256
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