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We study the zero-visibility cops and robbers game, where the robber is invisible to the cops until they are caught. This differs from the classic game where full information about the robber's location is known at any time. A previously…

Discrete Mathematics · Computer Science 2025-09-08 Igor Potapov , Tymofii Prokopenko , John Sylvester

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

We consider a game in which a cop searches for a moving robber on a graph using distance probes, studied by Carragher, Choi, Delcourt, Erickson and West, which is a slight variation on one introduced by Seager. Carragher, Choi, Delcourt,…

Combinatorics · Mathematics 2020-08-12 John Haslegrave , Richard A. B. Johnson , Sebastian Koch

The localization game is a two player combinatorial game played on a graph $G=(V,E)$. The cops choose a set of vertices $S_1 \subseteq V$ with $|S_1|=k$. The robber then chooses a vertex $v \in V$ whose location is hidden from the cops, but…

Combinatorics · Mathematics 2022-09-07 Lyuben Lichev , Dieter Mitsche , Pawel Pralat

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

We consider a variation of the Cops and Robber game where the cops can only see the robber when the distance between them is at most a fixed parameter $\ell$. We consider the basic consequences of this definition for some simple graph…

Discrete Mathematics · Computer Science 2017-08-25 N. E. Clarke , D. Cox , C. Duffy , D. Dyer , S. Fitzpatrick , M. E. Messinger

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

The localization game is a pursuit-evasion game analogous to Cops and Robbers, where the robber is invisible and the cops send distance probes in an attempt to identify the location of the robber. We present a novel graph parameter called…

Combinatorics · Mathematics 2021-05-21 Natalie C. Behague , Anthony Bonato , Melissa A. Huggan , Trent G. Marbach , Brittany Pittman

The localization game is a variant of the game of Cops and Robber in which the robber is invisible and moves between adjacent vertices, but the cops can probe any $k$ vertices of the graph to obtain the distance between probed vertices and…

Combinatorics · Mathematics 2026-02-10 Vesna Iršič Chenoweth , Matija Skrt

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 consider a game in which a cop searches for a moving robber on a graph using distance probes, which is a slight variation on one introduced by Seager. Carragher, Choi, Delcourt, Erickson and West showed that for any n-vertex graph $G$…

Combinatorics · Mathematics 2020-08-12 John Haslegrave , Richard A. B. Johnson , Sebastian Koch

We introduce a new variant of the game of Cops and Robbers played on graphs, where the robber is invisible unless outside the neighbor set of a cop. The hyperopic cop number is the corresponding analogue of the cop number, and we…

Combinatorics · Mathematics 2017-10-30 A. Bonato , N. E. Clarke , D. Cox , S. Finbow , F. Mc Inerney , M. E. Messinger

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

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

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

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

In the Localization game played on graphs, a set of cops uses distance probes to identify the location of an invisible robber. We present an extension of the game and its main parameter, the localization number, to directed graphs. We…

Combinatorics · Mathematics 2022-08-17 Anthony Bonato , Ryan Cushman , Trent G. Marbach , Brittany Pittman

We consider the well-studied cops and robbers game in the context of oriented graphs, which has received surprisingly little attention to date. We examine the relationship between the cop numbers of an oriented graph and its underlying…

\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 game of cops and robbers is a pursuit game on graphs where a set of agents, called the cops try to get to the same position of another agent, called the robber. Cops and robbers has been studies on several classes of graphs including…

Combinatorics · Mathematics 2019-03-19 Seyyed Aliasghar Hosseini , Masood Masjoody , Ladislav Stacho
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