English
Related papers

Related papers: General Cops and Robbers Games with randomness

200 papers

In the classic game of Cops and Robbers, a team of cops pursues a robber through a graph. The traditional model of Cops and Robbers operates under the assumption that the cops know the robber's location at all times. Recently, however,…

Combinatorics · Mathematics 2025-09-08 John Jones , William B. Kinnersley

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

The game of cops and robber is a pursuit-evasion game played on graphs that has been extensively studied. Traditionally the game is played with one or more cops and only one robber, but in this paper we consider the game played with…

Combinatorics · Mathematics 2025-09-15 Miha Gyergyek , Vesna Iršič Chenoweth

We study a variation of the classical pursuit-evasion game of Cops and Robbers in which agents are required to move to an adjacent vertex on every turn. We explore how the minimum number of cops needed to catch the robber can change when…

Combinatorics · Mathematics 2018-08-22 Ilya Gromovikov , William B. Kinnersley , Ben Seamone

Cops and Robber is a family of two-player games played on graphs in which one player controls a number of cops and the other player controls a robber. In alternating turns, each player moves (all) their figures. The cops try to capture the…

Combinatorics · Mathematics 2024-01-11 Minh Tuan Ha , Paul Jungeblut , Torsten Ueckerdt , Paweł Żyliński

We study a variant of the classical Cops and Robbers game with one cop and one robber, in which the cop follows a fixed walk on the graph, a patrol, that is chosen before the game begins, while the robber is omniscient, he knows the entire…

Combinatorics · Mathematics 2026-03-10 Nina Chiarelli , Paul Dorbec , Miloš Stojaković , Andrej Taranenko

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

We consider the Cops and Robber pursuit-evasion game when the edge-set of the graph is allowed to change in time, possibly at every round. Specifically, the game is played on an infinite periodic sequence $\mathcal{G} = (G_0, \dots,…

Discrete Mathematics · Computer Science 2024-10-31 Jean-Lou De Carufel , Paola Flocchini , Nicola Santoro , Frédéric Simard

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. $k$ 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

The 'Cheating Robot' version of Cops and Robbers is played on a finite, simple, connected graph. The players move in the same time period. However, before moving, the robot observes to which vertices the cops are moving and it is fast…

Combinatorics · Mathematics 2021-03-12 Melissa A. Huggan , Richard J. Nowakowski

Several variants of the cops and robbers (CR) game have been studied in the past. In this paper we examine a novel variant, which is played between two cops, each one independently trying to catch a "passive robber". We will call this the…

Discrete Mathematics · Computer Science 2016-11-22 Athanasios Kehagias , Georgios Konstantinidis

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 recently introduced variation of the game of cops and robber is played on geodesic spaces. In this paper we establish some general strategies for the players, in particular the generalized radial strategy and the covering space…

Metric Geometry · Mathematics 2022-11-07 Vesna Iršič , Bojan Mohar , Alexandra Wesolek

We introduce the game of Cops and Eternal Robbers played on graphs, where there are infinitely many robbers that appear sequentially over distinct plays of the game. A positive integer $t$ is fixed, and the cops are required to capture the…

Discrete Mathematics · Computer Science 2020-03-11 Anthony Bonato , Melissa Huggan , Trent Marbach , Fionn Mc Inerney

We consider a variant of the game of Cops and Robbers, called Lazy Cops and Robbers, where at most one cop can move in any round. We investigate the analogue of the cop number for this game, which we call the lazy cop number. Lazy Cops and…

Combinatorics · Mathematics 2013-12-09 Deepak Bal , Anthony Bonato , William B. Kinnersley , Paweł Prałat

We consider the Robber Locating Game, where an invisible moving robber tries to evade the pursuit of one or more helicopter cops, who send distance probes from anywhere on the graph. In this paper, we attempt to propose two useful…

Computational Complexity · Computer Science 2023-07-07 Shiqi Pan

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 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

We investigate multiple variants of the game Cops and Robbers. Playing it on an $n \times n$ toroidal chess graph, the game is varied by defining moves for cops and robbers differently, always mimicking moves of certain chess pieces. In…

Combinatorics · Mathematics 2018-10-26 Allyson Hahn , Neil R. Nicholson