An Invitation to Pursuit-Evasion Games and Graph Theory

A new book

by Anthony Bonato


Published by


Description: Graphs measure interactions between objects, from friendship links on Twitter, to transactions between Bitcoin users, and to the flow of energy in a food chain. While graphs statically represent interacting systems, they may also be used to model dynamic interactions. For example, imagine an invisible evader loose on a graph, leaving only behind breadcrumb clues to their whereabouts. You set out with pursuers of your own, seeking out the evader's location. Would you be able to detect their location? If so, then how many resources are needed for detection, and how fast can that happen? These basic-seeming questions point towards the broad conceptual framework of pursuit-evasion games played on graphs. Central to pursuit-evasion games on graphs is the idea of optimizing certain parameters, whether they are the cop number, burning number, or localization number, for example. This book would be excellent for a second course in graph theory at the undergraduate or graduate level. It surveys different areas in graph searching and highlights many fascinating topics intersecting classical graph theory, geometry, and combinatorial designs. Each chapter ends with approximately 20 exercises and around five larger scale projects.

Audience: Undergraduate and graduate students, pure and applied mathematicians, computer scientists, and all those interested in graph theory or networks.

Order soon from the AMS or Amazon.

Series: Student Mathematical Library


Excerpts from reviews:

"Overall, the book is reader friendly and engaging, with many helpful figures and illustrations. The author writes in the preface that the book aims to be "self-contained, understandable, and accessible to a broad mathematical audience," and it achieves that goal."

-Thomas Wiseman, for zbMATH Open.

Some pages from the book (pdf files):

Table of contents