Crossing Numbers of Graphs: 1st Edition (Hardback) book cover

Crossing Numbers of Graphs

1st Edition

By Marcus Schaefer

CRC Press

350 pages | 102 B/W Illus.

Purchasing Options:$ = USD
Hardback: 9781498750493
pub: 2017-12-05
SAVE ~$21.00
$105.00
$84.00
x
eBook (VitalSource) : 9781315152394
pub: 2018-01-02
from $28.98


FREE Standard Shipping!

Description

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.

The first part of the text deals with traditional crossing number, crossing number values, crossing lemma, related parameters, computational complexity, and algorithms. The second part includes the rich history of alternative crossing numbers, the rectilinear crossing number, the pair crossing number, and the independent odd crossing number.It also includes applications of the crossing number outside topological graph theory.

  • 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

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

About the Author

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.

About the Series

Discrete Mathematics and Its Applications

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
COM046000
COMPUTERS / Operating Systems / General
MAT000000
MATHEMATICS / General
MAT004000
MATHEMATICS / Arithmetic
MAT036000
MATHEMATICS / Combinatorics