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Crossing Numbers of Graphs: Discrete Mathematics and Its Applications

Autor Marcus Schaefer
en Limba Engleză Paperback – 21 ian 2023
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
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Specificații

ISBN-13: 9781032476445
ISBN-10: 1032476443
Pagini: 376
Ilustrații: 102
Dimensiuni: 156 x 234 mm
Greutate: 0.53 kg
Ediția:1
Editura: CRC Press
Colecția CRC Press
Seria Discrete Mathematics and Its Applications


Cuprins

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

Notă biografică



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.

Descriere

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 comput