Graphs and Cubes

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.

• Graphs and Cubes
• Sergei Ovchinnikov
• bipartite graphs
• cubical graphs
• partial cubes
• token systems

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)

• Dept. Mathematics, San Francisco State University, San Francisco, USA

  Sergei Ovchinnikov

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