Crossing Numbers of Graphs

Features

• Aimed at graduate students and professionals in both mathematics and computer science
• The first book of its kind devoted to the topic
• Authored by a noted authority in crossing numbers

Summary

Crossing Numbers of Graphs is the first book devoted to the crossing number, an increasingly popular object of study with surprising connections. The field has matured into a large body of work, which includes identifiable core results and techniques. The book presents a wide variety of ideas and techniques in topological graph theory, discrete geometry, and computer science.

Table of Contents

1. Introduction and History

Part I: The Crossing Number

2. Crossing Number

3. Crossing Number and other Parameters

4. Computational Complexity

5. Algorithms

Part II: Crossing Number Variants

6. Rectilinear Crossing Number

7. Local Crossing Number

8. Monotone and Book crossing numbers

9. Pair Crossing Number

10. k-planar Crossing Number

11. Independent Odd Crossing Number

12. Maximum Crossing Numbers

Part III: Applications

13. Crossing Minimization

14. Geometric Configurations

Appendix

A Topological Graph Theory Basics

B Complexity Theory

Author(s) Bio

Marcus Schaefer received his undergraduate degree from the University of Karlsruhe, then his Ph.D. in Computer Science from the University of Chicago. After getting his doctorate, he has worked at the Computer Science Department of DePaul University in Chicago where he became an associate professor. His research interests include graph drawing, graph theory, computational complexity, and computability. He currently has 57 publications on MathSciNet. He also co-authored a book, Algorithms.