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We introduce and study the Generalized Cops and Robbers game (GCR), an N-player pursuit game in graphs. The two-player version is essentially equivalent to the classic Cops and Robbers (CR) game. The three-player version can be understood…

Discrete Mathematics · Computer Science 2018-07-24 Athanasios Kehagias

We propose a definition of generalized Cops and Robbers games where there are two players, the Pursuer and the Evader, who each move via prescribed rules. If the Pursuer can ensure that the game enters into a fixed set of final positions,…

Combinatorics · Mathematics 2017-04-20 Anthony Bonato , Gary MacGillivray

The cops and robbers game has been extensively studied under the assumption of optimal play by both the cops and the robbers. In this paper we study the problem in which cops are chasing a drunk robber (that is, a robber who performs a…

Discrete Mathematics · Computer Science 2017-01-09 Athanasios Kehagias , Pawel Pralat

Cops and robbers is a pursuit-evasion game played on graphs. We completely classify the cop numbers for $n \times n$ knight graphs and queen graphs. This completes the classification of the cop numbers for all $n \times n$ classical chess…

We consider "surrounding" versions of the classic Cops and Robber game. The game is played on a connected graph in which two players, one controlling a number of cops and the other controlling a robber, take alternating turns. In a turn,…

Combinatorics · Mathematics 2024-10-14 Paul Jungeblut , Samuel Schneider , Torsten Ueckerdt

The game of Cops and Robber is a pursuit-evasion game which is usually played on a connected graph. In the game, a set of cops and a robber move around the vertices of a graph along edges, where the cops aim to capture the robber, while the…

Combinatorics · Mathematics 2021-07-27 Pinkaew Siriwong , Ratinan Boonklurb , Henry Liu , Sirirat Singhun

In this paper we study the two-player generalized Cops and Robber (GCR) games introduced by Bonato and MacGillivray. Our main goal is to present a full, self-contained game theoretic analysis of such games.

Combinatorics · Mathematics 2020-11-20 Athanasios Kehagias , Georgios Konstantinidis

\textsc{Cops and Robber} is one of the most studied two-player pursuit-evasion games played on graphs, where multiple \textit{cops}, controlled by one player, pursue a single \textit{robber}. The main parameter of interest is the…

Combinatorics · Mathematics 2023-07-04 Harmender Gahlawat , Zin Mar Myint , Sagnik Sen

The cops-and-robber (CR) game has been used in mobile robotics as a discretized model (played on a graph G) of pursuit/evasion problems. The "classic" CR version is a perfect information game: the cops' (pursuer's) location is always known…

Discrete Mathematics · Computer Science 2014-02-26 Athanasios Kehagias , Dieter Mitsche , Pawel Pralat

In this paper we study the concurrent cops and robber (CCCR) game. CCCR follows the same rules as the classical, turn-based game, except for the fact that the players move simultaneously. The cops' goal is to capture the robber and the…

Discrete Mathematics · Computer Science 2015-06-12 Georgios Konstantinidis , Athanasios Kehagias

Cops and robbers is a turn-based pursuit game played on a graph $G$. One robber is pursued by a set of cops. In each round, these agents move between vertices along the edges of the graph. The cop number $c(G)$ denotes the minimum number of…

Combinatorics · Mathematics 2011-09-09 Andrew Beveridge , Andrzej Dudek , Alan Frieze , Tobias Müller

Cops and robbers is a vertex-pursuit game played on graphs. In the classical cops-and-robbers game, a set of cops and a robber occupy the vertices of the graph and move alternately along the graph's edges with perfect information about each…

Discrete Mathematics · Computer Science 2018-06-12 Ziyuan Gao , Boting Yang

We introduce the game of Surrounding Cops and Robbers on a graph, as a variant of the original game of Cops and Robbers. In contrast to the original game in which the cops win by occupying the same vertex as the robber, they now win by…

Cops and Robbers is a pursuit-evasion game played on graphs, of which many variants have been developed and studied. We introduce a variant of this game, "Sneaky-Active Cops and Robbers", where all cops and robber must move on their turn,…

Combinatorics · Mathematics 2026-03-16 Tien Chih , Laura Scull

Cops and Robbers is a pursuit evasion game played on a graph, first introduced independently by Quilliot \cite{quilliot1978jeux} and Nowakowski and Winkler \cite{NOWAKOWSKI1983235} over four decades ago. A main interest in recent the…

Machine Learning · Computer Science 2026-02-19 Meagan Mann , Christian Muise , Erin Meger

\textsc{Cops and Robber} is a game played on graphs where a set of \textit{cops} aim to \textit{capture} the position of a single \textit{robber}. The main parameter of interest in this game is the \textit{cop number}, which is the minimum…

Combinatorics · Mathematics 2025-12-29 Harmender Gahlawat

Motivated by a biological scenario illustrated in the YouTube video \url{ https://www.youtube.com/watch?v=Z_mXDvZQ6dU} where a neutrophil chases a bacteria cell moving in random directions, we present a variant of the cop and robber game on…

Combinatorics · Mathematics 2020-04-02 Pamela Harris , Erik Insko , Alicia Prieto-Langarica , Rade Stoisavljevic , Shaun Sullivan

The game of Cops and Robbers is an important model for studying computational queries in pursuit-evasion environments, among others. As recent logical explorations have shown, its structure exhibits appealing analogies with modal logic. In…

Logic in Computer Science · Computer Science 2025-08-04 Dazhu Li , Sujata Ghosh , Fenrong Liu

The game of Cops and Robber is traditionally played on a finite graph. The purpose of this paper is to introduce and analyse the game that is played on an arbitrary geodesic space (a compact, path-connected space endowed with intrinsic…

Metric Geometry · Mathematics 2026-01-14 Bojan Mohar

The Cops and Robber game on geodesic spaces is a pursuit-evasion game with discrete steps which captures the behavior of the game played on graphs, as well as that of continuous pursuit-evasion games. One of the outstanding open problems…

Combinatorics · Mathematics 2024-02-09 Vesna Iršič , Bojan Mohar , Alexandra Wesolek
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