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Topics in Intersection Graph Theory

Topics in Intersection Graph Theory

Part of Monographs on Discrete Mathematics and Applications

  • Date Published: February 1999
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial null Mathematics for availability.
  • format: Paperback
  • isbn: 9780898714302


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About the Authors
  • Finally there is a book that presents real applications of graph theory in a unified format. This book is the only source for an extended, concentrated focus on the theory and techniques common to various types of intersection graphs. It is a concise treatment of the aspects of intersection graphs that interconnect many standard concepts and form the foundation of a surprising array of applications to biology, computing, psychology, matrices, and statistics. The authors emphasize the underlying tools and techniques and demonstrate how this approach constitutes a definite theory within graph theory. Some of the applications are not widely known or available in the graph theoretic literature and are presented here for the first time. The book also includes a detailed literature guide for many specialized and related areas, a current bibliography, and more than 100 exercises.

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    Product details

    • Date Published: February 1999
    • format: Paperback
    • isbn: 9780898714302
    • length: 213 pages
    • dimensions: 250 x 178 x 11 mm
    • weight: 0.384kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial null Mathematics for availability.
  • Table of Contents

    1. Intersection Graphs. Basic Concepts
    Intersection Classes
    Parsimonious Set Representations
    Clique Graphs
    Line Graphs
    2. Chordal Graphs. Chordal Graphs as Intersection Graphs
    Other Characterizations
    Tree Hypergraphs
    Some Applications of Chordal Graphs
    Split Graphs
    3. Interval Graphs. Definitions and Characterizations
    Interval Hypergraphs
    Proper Interval Graphs
    Some Applications of Interval Graphs
    4. Competition Graphs. Neighborhood Graphs
    Competition Graphs
    Interval Competition Graphs
    Upper Bound Graphs
    5. Threshold Graphs. Definitions and Characterizations
    Threshold Graphs as Intersection Graphs
    Difference Graphs and Ferrers Digraphs
    Some Applications of Threshold Graphs
    6. Other Kinds of Intersection. p-Intersection Graphs
    Intersection Multigraphs and Pseudographs
    Tolerance Intersection Graphs
    7. Guide to Related Topics. Assorted Geometric Intersection Graphs
    Bipartite Intersection Graphs, Intersection Digraphs, and Catch (Di)Graphs
    Chordal Bipartite and Weakly Chordal Graphs
    Circle Graphs and Permutation Graphs
    Clique Graphs of Chordal Graphs and Clique-Helly Graphs
    Containment, Comparability, Cocomparability, and Asteroidal Triple-Free Graphs
    Infinite Intersection Graphs
    Miscellaneous Topics
    P4-Free Chordal Graphs and Cographs
    Powers of Intersection Graphs
    Sphere-of-Influence Graphs
    Strongly Chordal Graphs

  • Authors

    Terry A. McKee

    F. R. McMorris

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