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Topics in Intersection Graph Theory

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by Terry A. McKee and F. R. McMorris


1999 / viii + 205 pages / Softcover / ISBN: 978-0-898714-30-2 / ISBN-10: 0-89871-430-3 / List Price $99.00 / SIAM Member Price $69.30 / Order Code DT02

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.

This book is written for students who have completed a basic graph theory course and for mathematicians seeking a guide for graph theory and graph modeling. Anyone working in applications of intersection graphs stands to gain a better understanding of the larger context of the field by reading this book.

Preface; Chapter 1: Intersection Graphs. Basic Concepts; Intersection Classes; Parsimonious Set Representations; Clique Graphs; Line Graphs; Hypergraphs; Chapter 2: Chordal Graphs. Chordal Graphs as Intersection Graphs; Other Characterizations; Tree Hypergraphs; Some Applications of Chordal Graphs; Split Graphs; Chapter 3: Interval Graphs. Definitions and Characterizations; Interval Hypergraphs; Proper Interval Graphs; Some Applications of Interval Graphs; Chapter 4: Competition Graphs. Neighborhood Graphs; Competition Graphs; Interval Competition Graphs; Upper Bound Graphs; Chapter 5: Threshold Graphs. Definitions and Characterizations; Threshold Graphs as Intersection Graphs; Difference Graphs and Ferrers Digraphs; Some Applications of Threshold Graphs; Chapter 6: Other Kinds of Intersection. p-Intersection Graphs; Intersection Multigraphs and Pseudographs; Tolerance Intersection Graphs; Chapter 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; Bibliography; Index.

ISBN: 9780898714302

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