The game of cops and robbers on graphs.

*(English)*Zbl 1298.91004
Student Mathematical Library 61. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-5347-4/pbk). xix, 276 p. (2011).

This is a textbook that presents the state of the art in the literature on cops and robber games and, more generally, vertex pursuit games on graphs. The cops and robber game was first introduced in the 1980s and there has been a growing literature on this topic. It is a two-player, zero-sum game where one player controls a set of cops and the other player controls the robber. The first player’s objective is to capture the robber. The game is played on a graph, cops and robber are restricted to vertices and they move each round to neighboring vertices. The book, which is written in a lively and highly readable fashion, is suitable for both advanced undergraduate and beginner graduate students, but it also covers advanced topics that will be of interest to researchers in mathematics, computer science and game theory. There are over 200 exercises in the book, with many worked out examples. Many open problems are listed throughout the book and a comprehensive set of references is provided.

Reviewer: Giacomo Bonanno (Davis)

##### MSC:

91-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to game theory, economics, and finance |

91A43 | Games involving graphs |

91A05 | 2-person games |

91A24 | Positional games (pursuit and evasion, etc.) |

05-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to combinatorics |

05C75 | Structural characterization of families of graphs |

05C57 | Games on graphs (graph-theoretic aspects) |

05C85 | Graph algorithms (graph-theoretic aspects) |

05C63 | Infinite graphs |

05C80 | Random graphs (graph-theoretic aspects) |