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

part 1|107 pages

The Crossing Number

chapter 1|30 pages

The Conjectures of Zarankiewicz and Hill

chapter 2|29 pages

Drawings and Values

chapter 3|23 pages

The Crossing Number and Other Parameters

chapter 4|21 pages

Complexity and Algorithms

part 2|185 pages

Crossing Number Variants

chapter 5|25 pages

The Rectilinear Crossing Number

Rectilinear and Pseudolinear Drawings

chapter 6|20 pages

The Rectilinear Crossing Number

Values and Bounds

chapter 7|24 pages

The Local Crossing Number

chapter 8|24 pages

Book and Monotone Crossing Numbers

chapter 9|16 pages

The Pair Crossing Number

chapter 10|14 pages

The k-planar Crossing Number

chapter 11|28 pages

The Independent Odd Crossing Number

chapter 12|31 pages

Maximum Crossing Numbers

part 3|19 pages


chapter Appendix A|11 pages

Basics of Topological Graph Theory

chapter Appendix B|5 pages

Basics of Complexity