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Efficient Graph Representations
Jeremy P. Spinrad, Vanderbilt University, Nashville, TN
A co-publication of the AMS and Fields Institute.
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Fields Institute Monographs
2003; 342 pp; hardcover
Volume: 19
ISBN-10: 0-8218-2815-0
ISBN-13: 978-0-8218-2815-1
List Price: US$105
Member Price: US$84
Order Code: FIM/19
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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 co-published 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
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