This monograph is the first to deal with graph representation as a field of study. It is written from both a mathematical and computer science perspective. Synthesizing the two traditions opens a number of interesting new research areas. Some individual classes of graphs are important but are not adequately covered in any current text. This book gives a much more current view of important algorithmic developments in intersection graph classes than is currently available and includes a large number of new open problems. It deals with the questions that arise from storing a graph in a computer. Different classes of graphs admit different forms of computer representations, and focusing on the representations gives a new perspective on a number of problems. For a variety of classes of graphs, the book considers such questions as existence of good representations, algorithms for finding representations, questions of characterizations in terms of representation, and how the representation affects the complexity of optimization problems. General models of efficient computer representations are also considered. The book is designed to be used both as a text for a graduate course on topics related to graph representation and as a monograph for anyone interested in research in the field of graph representation. The material is of interest both to those focusing purely on graph theory and to those working in the area of graph algorithms. Titles in this series are copublished with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada). Readership Graduate students and researchers interested in graph theory and computer science. Reviews "This book presents a fantastic encyclopedia of graph classes ..."  EMS Newsletter "The author's `Survey of results on graph classes' ... It is worth reading and mentions some interesting research problems ... an excellent research monograph that offers plenty of material ... The large number of exercises will be very helpful in teaching ... highly recommended by the reviewer."  Mathematical Reviews Table of Contents  Explanatory remarks
 Introduction
 Implicit representation
 Intersection and containment representations
 Real numbers in graph representations
 Classes which use global information
 Visibility graphs
 Intersection of graph classes
 Graph classes defined by forbidden subgraphs
 Chordal bipartite graphs
 Matrices
 Decomposition
 Elimination schemes
 Recognition algorithms
 Robust algorithms for optimization problems
 Characterization and construction
 Applications
 Glossary
 Survey of results on graph classes
 Bibliography
 Index
