Overview
- 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
Part of the book series: Universitext (UTX)
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Table of contents (8 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
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)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Graphs and Cubes
Authors: Sergei Ovchinnikov
Series Title: Universitext
DOI: https://doi.org/10.1007/978-1-4614-0797-3
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC 2011
Softcover ISBN: 978-1-4614-0796-6Published: 30 August 2011
eBook ISBN: 978-1-4614-0797-3Published: 30 August 2011
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XIII, 287
Number of Illustrations: 172 b/w illustrations
Topics: Graph Theory