Schaefer Crossing Numbers of Graphs

1. Auflage 2017
ISBN: 978-1-4987-5050-9
Verlag: CRC Press
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 376 Seiten

Reihe: Discrete Mathematics and Its Applications

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.

Autoren/Hrsg.

Schaefer, Marcus

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
• Mathematik | Informatik EDV | Informatik Betriebssysteme
• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

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

Über Autor(innen)

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 School of Computing of DePaul University in Chicago where he is now a full 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.