Crossing Numbers of Graphs

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 scienceThe first book of its kind devoted to the topicAuthored by a noted authority in crossing numbers

1. Introduction and HistoryPart I: The Crossing Number2. Crossing Number3. Crossing Number and other Parameters4. Computational Complexity5. AlgorithmsPart II: Crossing Number Variants6. Rectilinear Crossing Number7. Local Crossing Number8. Monotone and Book crossing numbers9. Pair Crossing Number10. k-planar Crossing Number11. Independent Odd Crossing Number12. Maximum Crossing NumbersPart III: Applications13. Crossing Minimization14. Geometric ConfigurationsAppendixA Topological Graph Theory BasicsB 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 has57 publications on MathSciNet. He also co-authored a book, Algorithms.