Efficient graph representations

Includes index

Includes bibliography (p. 319- 342)and references.

1. Introduction
2. Implicit representation
3. Intersection and containment representations
4. Real numbers in graph representations
5. Classes which use global information
6. Visibility graphs
7. Intersection of graph classes
8. Graph classes defined by forbidden subgraphs
9. Chordal bipartite graphs
10. Matrices
11. Decomposition
12. Elimination schemes
13. Recognition algorithms
14. Robust algorithms for optimization problems
15. Characterization and construction
16. Applications

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.