SpringerBriefs in Optimization

Topics in Matroid Theory

Authors: Pitsoulis, Leonidas S.

  • ​​​​​Provides a sollid introduction to matroid theory
  • Present results in matroid theory as they appear in the context of combinatorial optimization​
  • Contains a strong emphasis on algorithmic consequences of matroid theory
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eBook $39.99
price for USA (gross)
  • ISBN 978-1-4614-8957-3
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  • Immediate eBook download after purchase
Softcover $54.99
price for USA
  • ISBN 978-1-4614-8956-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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  • Rental duration: 1 or 6 month
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About this book

Topics in Matroid Theory provides a brief introduction to matroid theory with an emphasis on algorithmic consequences.Matroid theory is at the heart of combinatorial optimization and has attracted various pioneers such as Edmonds, Tutte, Cunningham and Lawler among others. Matroid theory encompasses matrices, graphs and other combinatorial entities under a common, solid algebraic framework, thereby providing the analytical tools to solve related difficult algorithmic problems. The monograph contains a rigorous axiomatic definition of matroids along with other necessary concepts such as duality, minors, connectivity and representability as demonstrated in matrices, graphs and transversals. The author also presents a deep decomposition result in matroid theory that provides  a structural characterization of graphic matroids, and show how this can be extended to signed-graphic matroids, as well as the immediate algorithmic consequences.  

Reviews

“The clear and concise style and the well chosen examples illustrating concepts, theorems and algorithms make this book a valuable resource for graduate students and researchers interested in theoretical and algorithmic applications of matroid theory.” (Brigitte Servatius, zbMATH 1319.05033, 2015)

“The goal of the book is to introduce a decomposition theorem providing a characterization of graphic and signed-graphic matroids. … The monograph is recommended basically to master or PhD students. … The book has a very logical structure which helps the reader to understand the whole issue.” (Bálint Márk Vásárhelyi, Acta Scientiarum Mathematicarum, Vol. 80 (3-4), 2014)

Table of contents (6 chapters)

  • Introduction

    Pitsoulis, Leonidas

    Pages 1-4

  • Graph Theory, Vector Spaces, and Transversals

    Pitsoulis, Leonidas

    Pages 5-24

  • Definition of Matroids

    Pitsoulis, Leonidas

    Pages 25-45

  • Representability, Duality, Minors, and Connectivity

    Pitsoulis, Leonidas

    Pages 47-73

  • Decomposition of Graphic Matroids

    Pitsoulis, Leonidas

    Pages 75-100

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-1-4614-8957-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA
  • ISBN 978-1-4614-8956-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Topics in Matroid Theory
Authors
Series Title
SpringerBriefs in Optimization
Copyright
2014
Publisher
Springer-Verlag New York
Copyright Holder
Leonidas S. Pitsoulis
eBook ISBN
978-1-4614-8957-3
DOI
10.1007/978-1-4614-8957-3
Softcover ISBN
978-1-4614-8956-6
Series ISSN
2190-8354
Edition Number
1
Number of Pages
XIV, 127
Number of Illustrations and Tables
46 b/w illustrations
Topics