Crossing Numbers of Graphs

Crossing Numbers of Graphs is the first book dedicated to the crossing number, a popular object of study with surprising connections. It presents a wide variety of ideas and techniques in topological graph theory, discrete geometry, and computer science, with a focus on traditional and alternative crossing numbers, their applications, and computational complexity.

Format: Paperback / softback
Length: 376 pages
Publication date: 21 January 2023
Publisher: Taylor & Francis Ltd

Crossing Numbers of Graphs is a comprehensive and groundbreaking work that delves into the world of crossing numbers, a fascinating object of study with remarkable connections. This field has grown exponentially, encompassing a vast body of work that includes identifiable core results and innovative techniques. The book presents a diverse range of ideas and methodologies in topological graph theory, discrete geometry, and computer science, offering a comprehensive understanding of this interdisciplinary domain.

In the first part of the text, the authors explore traditional crossing numbers, their values, crossing lemmas, related parameters, computational complexity, and various algorithms. They provide a solid foundation for understanding the fundamental concepts and applications of crossing numbers.

The second part of the book takes readers on a captivating journey through the rich history of alternative crossing numbers. It discusses the rectilinear crossing number, the pair crossing number, and the independent odd crossing number, each with its unique properties and applications. The authors also explore the broader realm of crossing numbers beyond topological graph theory, showcasing their relevance in diverse fields such as combinatorics, coding theory, and geometric group theory.

This book is meticulously crafted for graduate students and professionals seeking to delve into the intricate world of crossing numbers. Authored by a renowned authority in the field, Crossing Numbers of Graphs offers a comprehensive and up-to-date exploration of this topic. With its clear explanations, insightful examples, and extensive references, it serves as a valuable resource for scholars and practitioners alike.

By unraveling the mysteries of crossing numbers, this book opens up new avenues for research and innovation in mathematics and computer science. It demonstrates the power of interdisciplinary collaboration and sheds light on the exciting connections between seemingly disparate fields. As the field continues to evolve, Crossing Numbers of Graphs will remain a cornerstone for anyone seeking to advance their understanding of this captivating mathematical object.

Weight: 700g
Dimension: 234 x 156 (mm)
ISBN-13: 9781032476445