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Related papers: Containment: A Variation of Cops and Robbers

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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 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 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

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 consider the new game of Cops and Attacking Robbers, which is identical to the usual Cops and Robbers game except that if the robber moves to a vertex containing a single cop, then that cop is removed from the game. We study the minimum…

\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

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 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

In this short paper we study the game of cops and robbers, which is played on the vertices of some fixed graph $G$. Cops and a robber are allowed to move along the edges of $G$ and the goal of cops is to capture the robber. The cop number…

Combinatorics · Mathematics 2010-04-13 Alex Scott , Benny Sudakov

In the game of Cops and Robber, a team of cops attempts to capture a robber on a graph $G$. Initially, all cops occupy some vertices in $G$ and the robber occupies another vertex. In each round, a cop can move to one of its neighbors or…

Combinatorics · Mathematics 2019-09-02 Mingrui Liu

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

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 the game of Cops and Robbers, a team of cops attempts to capture a robber on a graph $G$. All players occupy vertices of $G$. The game operates in rounds; in each round the cops move to neighboring vertices, after which the robber does…

Combinatorics · Mathematics 2018-06-20 William B. Kinnersley

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 the classic cop and robber game, two players--the cop and the robber--take turns moving to a neighboring vertex or staying at their current position. The cop aims to capture the robber, while the robber tries to evade capture. A graph…

Combinatorics · Mathematics 2025-02-17 Tanja Dravec , Vesna Iršič Chenoweth , Andrej Taranenko

Cops and Robbers is a well-studied pursuit-evasion game in which a set of cops seeks to catch a robber in a graph G, where cops and robber move along edges of G. The cop number of G is the minimum number of cops that is sufficient to catch…

The Cops and Robber game 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 they can catch the robber. The minimum number of cops needed…

Combinatorics · Mathematics 2013-12-30 Nancy E. Clarke , Samuel Fiorini , Gwenaël Joret , Dirk Oliver Theis

We consider a variation of cop vs.\ robber on graph in which the robber is not restricted by the graph edges; instead, he picks a time-independent probability distribution on $V(G)$ and moves according to this fixed distribution. The cop…

Combinatorics · Mathematics 2013-08-23 Natasha Komarov , Peter Winkler

The game of cops and robbers is played on a fixed (finite or infinite) graph $G$. The cop chooses his starting position, then the robber chooses his. After that, they take turns and move to adjacent vertices, or stay at their current…

Combinatorics · Mathematics 2025-07-31 Tomáš Flídr , Maria-Romina Ivan

Cops and Robbers is a type of pursuit-evasion game played on a graph where a set of cops try to capture a single robber. The cops first choose their initial vertex positions, and later the robber chooses a vertex. The cops and robbers make…

Discrete Mathematics · Computer Science 2024-09-25 Prosenjit Bose , Jean-Lou De Carufel , Anil Maheshwari , Karthik Murali
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