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