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
Reihe
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Illustrationen
102 s/w Abbildungen
102 Illustrations, black and white
Maße
Höhe: 234 mm
Breite: 156 mm
Gewicht
ISBN-13
978-1-032-47644-5 (9781032476445)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
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.
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
