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Efficient Graph Representations
 
Jeremy P. Spinrad Vanderbilt University, Nashville, TN
A co-publication of the AMS and Fields Institute
Efficient Graph Representations
eBook ISBN:  978-1-4704-3146-4
Product Code:  FIM/19.E
List Price: $111.00
MAA Member Price: $99.90
AMS Member Price: $88.80
Efficient Graph Representations
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Efficient Graph Representations
Jeremy P. Spinrad Vanderbilt University, Nashville, TN
A co-publication of the AMS and Fields Institute
eBook ISBN:  978-1-4704-3146-4
Product Code:  FIM/19.E
List Price: $111.00
MAA Member Price: $99.90
AMS Member Price: $88.80
  • Book Details
     
     
    Fields Institute Monographs
    Volume: 192003; 342 pp
    MSC: 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 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.

  • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 192003; 342 pp
MSC: 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 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.

  • 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
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.