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We consider the game of Zombies and Survivors as introduced by Fitzpatrick, Howell, Messinger and Pike (2016) This is a variation of the game Cops and Robber where the zombies (in the cops' role) are of limited intelligence and will always…

Combinatorics · Mathematics 2018-06-13 Shannon L. Fitzpatrick

We consider a new probabilistic graph searching game played on graphs, inspired by the familiar game of Cops and Robbers. In Zombies and Survivors, a set of zombies attempts to eat a lone survivor loose on a given graph. The zombies…

Discrete Mathematics · Computer Science 2015-03-31 Anthony Bonato , Dieter Mitsche , Xavier Pérez-Giménez , Paweł Prałat

We compare two kinds of pursuit-evasion games played on graphs. In Cops and Robbers, the cops can move strategically to adjacent vertices as they please, while in a new variant, called deterministic Zombies and Survivors, the zombies (the…

Combinatorics · Mathematics 2018-09-11 David Offner , Kerry Ojakian

We study zombies and survivor, a variant of the game of cops and robber on graphs. In this variant, the single survivor plays the role of the robber and attempts to escape from the zombies that play the role of the cops. The zombies are…

Combinatorics · Mathematics 2022-04-27 Prosenjit Bose , Jean-Lou De Carufel , Thomas Shermer

The game of Cops and Robbers is a pursuit-evasion game on graphs that has been extensively studied in finite settings, particularly through the concept of cop number. In this paper, we explore infinite variants of the game, focusing on the…

Combinatorics · Mathematics 2025-09-04 Kenzie Fontenot , Iris Nguyen , Cody Olsen

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

The two-player, complete information game of Cops and Robber is played on undirected finite graphs. A number of cops and one robber are positioned on vertices and take turns in sliding along edges. The cops win if, after a move, a cop and…

Combinatorics · Mathematics 2021-12-23 Gwenaël Joret , Marcin Kamiński , Dirk Oliver Theis

Cops and Robbers is a game played on a graph where a set of cops attempt to capture a single robber. The game proceeds in rounds, where each round first consists of the cops' turn, followed by the robber's turn. In the cops' turn, every cop…

Discrete Mathematics · Computer Science 2025-07-03 Prosenjit Bose , Pat Morin , Karthik Murali

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

In Zombies and Survivors, a set of zombies attempts to eat a lone survivor loose on a given graph. The zombies randomly choose their initial location, and during the course of the game, move directly toward the survivor. At each round, they…

Combinatorics · Mathematics 2017-03-29 Pawel Pralat

We consider a variant of the game of Cops and Robbers, called Containment, in which cops move from edge to adjacent edge, the robber moves from vertex to adjacent vertex (but cannot move along an edge occupied by a cop). The cops win by…

Combinatorics · Mathematics 2015-05-08 Pawel Pralat

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

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…

We investigate a cops and robber game on directed graphs, where the robber moves along the arcs of the graph, while the cops can select any position at each time step. Our main focus is on the cop number: the minimum number of cops required…

Computational Complexity · Computer Science 2024-10-08 Walid Ben-Ameur , Alessandro Maddaloni

We consider "Containment": a variation of the graph pursuit game of Cops and Robber in which cops move from edge to adjacent edge, the robber moves from vertex to adjacent vertex (but cannot move along an edge occupied by a cop), and the…

Combinatorics · Mathematics 2019-03-19 Danny Crytser , Natasha Komarov , John Mackey

We study the vertex pursuit game of \emph{Cops and Robbers}, in which cops try to capture a robber on the vertices of the graph. The minimum number of cops required to win on a given graph $G$ is called the cop number of $G$. We focus on…

Combinatorics · Mathematics 2014-06-12 Noga Alon , Pawel Pralat

The Cops and Robber game is played on undirected finite graphs. $k$ cops and one robber are positioned on vertices and take turn in moving along edges. The cops win if, after a move, a cop and the robber are on the same vertex. A graph is…

Combinatorics · Mathematics 2011-11-10 Dirk Oliver Theis

\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

We introduce two variations of the cops and robber game on graphs. These games yield two invariants in $\mathbb{Z}_+\cup\{\infty\}$ for any connected graph $\Gamma$, the {weak cop number $\mathsf{wcop}(\Gamma)$} and the {strong cop number…

Combinatorics · Mathematics 2023-06-22 Jonathan Lee , Eduardo Martínez-Pedroza , Juan Felipe Rodríguez-Quinche

\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
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