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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

We study versions of cop and robber pursuit-evasion games on the visibility graphs of polygons, and inside polygons with straight and curved sides. Each player has full information about the other player's location, players take turns, and…

Computational Geometry · Computer Science 2016-01-07 Anna Lubiw , Jack Snoeyink , Hamideh Vosoughpour

The guarding game is a game in which several cops try to guard a region in a (directed or undirected) graph against Robber. Robber and the cops are placed on the vertices of the graph; they take turns in moving to adjacent vertices (or…

Computer Science and Game Theory · Computer Science 2013-11-15 R. Samal , T. Valla

Cops and robbers is a game between two players, where one tries to catch the other by moving along the edges of a graph. It is well known that on a finite graph the cop has a winning strategy if and only if the graph is constructible and…

Combinatorics · Mathematics 2015-03-31 Florian Lehner

The traditional game of cops and robbers is played on undirected graph. Recently, the same game played on directed graph is getting attention by more and more people. We knew that if we forbid some subgraph we can bound the cop number of…

Combinatorics · Mathematics 2020-01-29 Mingrui Liu

(abstract shortened to meet arxiv's length requirements) We investigate two variants of the classical Cops and robber game in graphs, recently introduced by Lee, Mart\'inez-Pedroza, and Rodr\'iguez-Quinche. The two versions are played in…

Combinatorics · Mathematics 2026-02-24 Louis Esperet , Harmender Gahlawat , Ugo Giocanti

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

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

The game of \emph{Cops and Robber} is usually played on a graph, where a group of cops attempt to catch a robber moving along the edges of the graph. The \emph{cop number} of a graph is the minimum number of cops required to win the game.…

Combinatorics · Mathematics 2024-04-29 Joshua Erde , Mihyun Kang , Florian Lehner , Bojan Mohar , Dominik Schmid

We consider a game in which a cop searches for a moving robber on a connected 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…

Combinatorics · Mathematics 2017-11-23 John Haslegrave , Richard A. B. Johnson , Sebastian Koch

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…

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 the cops and robber game, there are multiple cops and a single robber taking turns moving along the edges of a graph. The goal of the cops is to capture the robber (move to the same vertex as the robber) and the goal of the robber is to…

Combinatorics · Mathematics 2024-12-04 Suryaansh Jain , Subrahmanyam Kalyanasundaram , Kartheek Sriram Tammana

In the classical cop and robber game, two players, the cop C and the robber R, move alternatively along edges of a finite graph G. The cop captures the robber if both players are on the same vertex at the same moment of time. A graph G is…

Discrete Mathematics · Computer Science 2015-03-17 Jérémie Chalopin , Victor Chepoi , Nicolas Nisse , Yann Vaxès

\textit{Pursuit-evasion games} have been intensively studied for several decades due to their numerous applications in artificial intelligence, robot motion planning, database theory, distributed computing, and algorithmic theory.…

Discrete Mathematics · Computer Science 2023-07-11 Harmender Gahlawat , Meirav Zehavi

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 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 game of Cops and Robbers is a well known game played on graphs. In this paper we consider the class of graphs of bounded diameter. We improve the strategy of cops and previously used probabilistic method which results in an improved…

Combinatorics · Mathematics 2019-12-17 Seyyed Aliasghar Hosseini , Fiachra Knox , Bojan Mohar

In this paper, we study the game of cops and robber on the class of graphs with no even hole (induced cycle of even length) and claw (a star with three leaves). The cop number of a graph $G$ is defined as the minimum number of cops needed…

Combinatorics · Mathematics 2022-01-12 Ramin Javadi , Ali Momeni

In this paper, we study different variants of the Cops-and-Robber game with respect to cop- and robber\-/monotonicity. We study a visible and invisible robber and variants where the robber is lazy, thus can only move when the cops announce…

Discrete Mathematics · Computer Science 2025-02-24 Eva Fluck , David Philipps
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