eBook ISBN:  9781470431464 
Product Code:  FIM/19.E 
List Price:  $111.00 
MAA Member Price:  $99.90 
AMS Member Price:  $88.80 
eBook ISBN:  9781470431464 
Product Code:  FIM/19.E 
List Price:  $111.00 
MAA Member Price:  $99.90 
AMS Member Price:  $88.80 

Book DetailsFields Institute MonographsVolume: 19; 2003; 342 ppMSC: Primary 05; 68
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).
ReadershipGraduate students and researchers interested in graph theory and computer science.

Table of Contents

Chapters

Explanatory remarks

Chapter 1. Introduction

Chapter 2. Implicit representation

Chapter 3. Intersection and containment representations

Chapter 4. Real numbers in graph representations

Chapter 5. Classes which use global information

Chapter 6. Visibility graphs

Chapter 7. Intersection of graph classes

Chapter 8. Graph classes defined by forbidden subgraphs

Chapter 9. Chordal bipartite graphs

Chapter 10. Matrices

Chapter 11. Decomposition

Chapter 12. Elimination schemes

Chapter 13. Recognition algorithms

Chapter 14. Robust algorithms for optimization problems

Chapter 15. Characterization and construction

Chapter 16. Applications


Additional Material

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


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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 copublished with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
Graduate students and researchers interested in graph theory and computer science.

Chapters

Explanatory remarks

Chapter 1. Introduction

Chapter 2. Implicit representation

Chapter 3. Intersection and containment representations

Chapter 4. Real numbers in graph representations

Chapter 5. Classes which use global information

Chapter 6. Visibility graphs

Chapter 7. Intersection of graph classes

Chapter 8. Graph classes defined by forbidden subgraphs

Chapter 9. Chordal bipartite graphs

Chapter 10. Matrices

Chapter 11. Decomposition

Chapter 12. Elimination schemes

Chapter 13. Recognition algorithms

Chapter 14. Robust algorithms for optimization problems

Chapter 15. Characterization and construction

Chapter 16. Applications

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