An Invitation to Pursuit-Evasion Games and Graph Theory
A new book
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
Reviews:
"The text is primarily intended to support a one-semester course for graduate students or outstanding undergraduates who have already taken a class on graph theory.
It could also be a useful entrance point for mathematicians who want an overview of pursuit-evasion games. The author provides many exercises, as well as several suggestions for more ambitious research projects.
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.
"As a whole, it's remarkable how Dr. Bonato has distilled a huge body of literature into an extensively referenced 250 page book that could have easily been at least twice that length.
Researchers will surely find this a helpful reference text, with lots of important results and proofs conveniently organized in one place, but they are also likely to encounter something new and interesting, and probably an open problem or two to ponder.
Meanwhile, those who are newer to exploring these topics will almost certainly find at least one motivating idea --- a particular application or an entry point into the theory --- that gets them hooked into reading more.
-Brendan W. Sullivan, The American Mathematical Monthly
Some pages from the book (pdf files):