Terry McKee Home Terry A McKee

Department of Mathematics and Statistics Department of Mathematics and Statistics

College of Science and Mathematics College of Science and Mathematics

Wright State Home Wright State Home

 

Professor Emeritus, Mathematics and Statistics
Wright State University
3640 Colonel Glenn Highway
Dayton OH 45435-0001


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  Topics in Intersection Graph Theory by TA McKee and FR McMorris  

Topics in intersection graph theory

[SIAM Monographs on Discrete Mathematics and Applications #2]
Terry A. McKee and F.R. McMorris.
Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1999, vii+205 pp.

ISBN: 0-89871-430-3
QA 166.105.M34

 

Chapter 1: Intersection Graphs

1.1   Basic Concepts
1.2   Intersection Classes
1.3   Parsimonious Set Representations
1.4   Clique Graphs
1.5   Line Graphs
1.6   Hypergraphs

Chapter 2: Chordal Graphs

2.1   Chordal Graphs as Intersection Graphs
2.2   Other Characterizations
2.3   Tree Hypergraphs
2.4   Some Applications of Chordal Graphs

2.4.1   Applications to Biology
2.4.2   Applications to Computing
2.4.3   Applications to Matrices
2.4.4   Applications to Statistics

2.5   Split Graphs

Chapter 3: Interval Graphs

3.1   Definitions and Characterizations
3.2   Interval Hypergraphs
3.3   Proper Interval Graphs
3.4   Some Applications of Interval Graphs

3.4.1   Applications to Biology
3.4.2   Applications to Psychology
3.4.3   Applications to Computing

Chapter 4: Competition Graphs

4.1   Neighborhood Graphs
4.2   Competition Graphs

4.2.1   Squared Graphs
4.2.2   Two-Step Graphs

4.3   Interval Competition Graphs
4.4   Upper Bound Graphs

Chapter 5: Threshold Graphs

5.1   Definitions and Characterizations
5.2   Threshold Graphs as Intersection Graphs
5.3   Difference Graphs and Ferrers Digraphs
5.4   Some Applications of Threshold Graphs

Chapter 6: Other Kinds of Intersection

6.1   p-Intersection Graphs
6.2   Intersection Multigraphs and Pseudographs
6.3   Tolerance Intersection Graphs

Chapter 7: Guide to Related Topics

7.1   Assorted Geometric Intersection Graphs
7.2   Bipartite Intersection Graphs, Intersection Digraphs and Catch (Di)Graphs
7.3   Chordal Bipartite and Weakly Chordal Graphs
7.4   Circle Graphs and Permutation Graphs
7.5   Clique Graphs of Chordal Graphs and Clique-Helly Graphs
7.6   Containment, Comparability, Cocomparability, and Asteroidal Triple-Free Graphs
7.7   Infinite Intersection Graphs
7.8   Miscellaneous Topics
7.9   P_4-Free Chordal Graphs and Cographs
7.10  Powers of Intersection Graphs
7.11  Sphere-of-Influence Graphs
7.12  Strongly Chordal Graphs

Bibliography

Index

Publisher's Description and Ordering Information

Corrections and Updates

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Terry A McKee home page
Course information  | Brief vita
Topics in Intersection Graph Theory
corrections/updates; ordering information and review
Intersection graphs | Graph duality  | Graph meta-theory | Miscellaneous graph theory | Mathematical logic | Truly miscellaneous

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This web site was last updated December 29, 2001.
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