Издательство Springer, 2011, -302 pp.This book is an introductory text in graph theory, focusing on partial cubes, that is, graphs that are isometrically embeddable into hypercubes of an arbitrary dimension. This branch of graph theory has developed rapidly during the past three decades, producing exciting results and establishing links to other branches of mathematics. Because of their rich structural properties, partial cubes have found applications in theoretical computer science, coding theory, data transmission, genetics, and even the political and social sciences. However, this research area has previously failed to trickle down into graduate-level teaching of graph theory. In fact, even the term partial cube can’t be found in standard textbooks on graph theory. In this book, I attempt to remedy this situation. Exercising a concrete approach to graph theory, this book focuses on three classes of graphs: bipartite graphs, cubical graphs, and partial cubes (introduced in Chapters 2, 4, and 5, respectively). Cubical graphs are graphs that are embeddable into hypercubes; if they are isometrically embeddable into hypercubes, then they are called partial cubes. Cubical graph theory is a branch of graph theory that is reasonably small, yet deep enough to demonstrate the power and tools of the general theory. It can serve as a launching pad for studies of other topics in graph theory and their applications.Graphs Bipartite Graphs Cubes Cubical Graphs Partial Cubes Lattice Embeddings Hyperplane Arrangements Token Systems
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