Graphs measure interactions between objects such as friendship links on Twitter, transactions between Bitcoin users, and 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 twenty exercises and five larger scale projects.
Author(s): Anthony Bonato
Edition: 1
Publisher: American Mathematical Society
Year: 2022
Language: English
Pages: 254
Tags: Graph Theory; Graph Searching; Graph Burning; Pursuit-Evasion Games
Cover
Title page
Copyright page
Dedication
Contents
List of figures
Preface
Introduction
Cops and robbers
Graph searching
Graph burning
The localization game
Firefighter
Invisible robber games
Variants of pursuit-evasion games
Bibliography
Index
Other titles in this series
Back Cover
