Universitext

Graphs and Cubes

Authors: Ovchinnikov, Sergei

  • This is the only book available on the market that presents a comprehensive coverage of cubical graph and partial cube theories
  • Aimed towards lower-division graduate students in mathematics, but could be of interest to researchers using cubical graph and partial cube theories in mathematics and applications
  • Has applications in theoretical computer science, coding theory, data transmission, genetics, and even the political and social sciences
  • With its numerous illustrations and exercises, this presentation of partial cubes theory is student-friendly
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Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-1-4614-0797-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $74.95
price for USA
  • ISBN 978-1-4614-0796-6
  • 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
About this Textbook

This introductory text in graph theory focuses on partial cubes, which are graphs that are isometrically embeddable into hypercubes of an arbitrary dimension, as well as bipartite graphs, and cubical graphs. This branch of graph theory has developed rapidly during the past three decades, producing exciting results and establishing links to other branches of mathematics.

 

Currently, Graphs and Cubes is the only book available on the market that presents a comprehensive coverage of cubical graph and partial cube theories.  Many exercises, along with historical notes, are included at the end of every chapter, and readers are encouraged to explore the exercises fully, and use them as a basis for research projects.

 

The prerequisites for this text include familiarity with basic mathematical concepts and methods on the level of undergraduate courses in discrete mathematics, linear algebra, group theory, and topology of Euclidean spaces. While the book is intended for lower-division graduate students in mathematics, it will be of interest to a much wider audience; because of their rich structural properties, partial cubes appear in theoretical computer science, coding theory, genetics, and even the political and social sciences.

About the authors

Sergei Ovchinnikov is currently a mathematics professor at San Francisco State University.

Reviews

From the reviews:

“This book focuses on a class of bipartite graphs known as partial cubes, which are subgraphs of hypercubes (cubes) that allow isometric embeddings into a cube. … the book is aimed at lower-level graduate students. … Ample problems … as well as historic notes and suggested reading are available at the end of each chapter. … Overall, it is a good development of the subject. Summing Up: Recommended. Upper-division undergraduates and above.” (J. R. Burke, Choice, Vol. 49 (9), May, 2012)


Table of contents (8 chapters)

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-1-4614-0797-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $74.95
price for USA
  • ISBN 978-1-4614-0796-6
  • 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
Graphs and Cubes
Authors
Series Title
Universitext
Copyright
2011
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-1-4614-0797-3
DOI
10.1007/978-1-4614-0797-3
Softcover ISBN
978-1-4614-0796-6
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XIII, 287
Number of Illustrations and Tables
172 b/w illustrations
Topics