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9780898714302

Topics in Intersection Graph Theory

by ;
  • ISBN13:

    9780898714302

  • ISBN10:

    0898714303

  • Format: Paperback
  • Copyright: 1999-04-01
  • Publisher: Society for Industrial & Applied

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Summary

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.

Table of Contents

Preface
Intersection Graphs
Basic Concepts
Intersection Classes
Parsimonious Set Representations
Clique Graphs
Line Graphs
Hypergraphs
Chordal Graphs
Chordal Graphs as Intersection Graphs
Other Characterizations
Tree Hypergraphs
Some Applications of Chordal Graphs
Split Graphs
Interval Graphs
Definitions and Characterizations
Interval Hypergraphs
Proper Interval Graphs
Some Applications of Interval Graphs
Competition Graphs
Neighborhood Graphs
Competition Graphs
Interval Competition Graphs
Upper Bound Graphs
Threshold Graphs
Definitions and Characterizations
Threshold Graphs as Intersection Graphs
Difference Graphs and Ferrers Digraphs
Some Applications of Threshold Graphs
Other Kinds of Intersection
p-Intersection Graphs
Intersection Multigraphs and Pseudographs
Tolerance Intersection Graphs
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
Bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.

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