1st Edition

Crossing Numbers of Graphs

By Marcus Schaefer Copyright 2018
    376 Pages 102 B/W Illustrations
    by CRC Press

    376 Pages 102 B/W Illustrations
    by CRC Press

    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

    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


    A Topological Graph Theory Basics

    B Complexity Theory


    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.