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Related papers: Selfish Cops and Passive Robber: Qualitative Games

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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

\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 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

We theoretically analyze the Cops and Robber Game for the first time in a multidimensional grid. It is shown that for an $n$-dimensional grid, at least $n$ cops are necessary to ensure capture of the robber. We also present a set of cop…

Discrete Mathematics · Computer Science 2015-06-12 Sayan Bhattacharya , Goutam Paul , Swagato Sanyal

This paper considers the Cops and Attacking Robbers game, a variant of Cops and Robbers, where the robber is empowered to attack a cop in the same way a cop can capture the robber. In a graph $G$, the number of cops required to capture a…

Combinatorics · Mathematics 2024-08-06 Alexander Clow , Melissa A. Huggan , M. E. Messinger

We consider a variant of the Cops and Robber game, introduced by Fomin, Golovach, Kratochvil, in which the robber has unbounded speed, i.e. can take any path from her vertex in her turn, but she is not allowed to pass through a vertex…

Combinatorics · Mathematics 2011-04-19 Abbas Mehrabian

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

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…

In this short paper we study the game of Cops and Robbers, played on the vertices of some fixed graph $G$ of order $n$. The minimum number of cops required to capture a robber is called the cop number of $G$. We show that the cop number of…

Combinatorics · Mathematics 2014-09-30 Zsolt Adam Wagner

The Cops and Robber game on geodesic spaces is a pursuit-evasion game with discrete steps which captures the behavior of the game played on graphs, as well as that of continuous pursuit-evasion games. One of the outstanding open problems…

Combinatorics · Mathematics 2024-02-09 Vesna Iršič , Bojan Mohar , Alexandra Wesolek

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

Motivated by authentication, intrusion and spam detection applications we consider single-class classification (SCC) as a two-person game between the learner and an adversary. In this game the learner has a sample from a target distribution…

Machine Learning · Computer Science 2010-10-22 Ran El-Yaniv , Mordechai Nisenson

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

We consider a variant of Cops and Robbers in which both the cops and the robber are allowed to traverse up to $s$ edges on each of their turns, where $s \ge 2$. We give several general for this new model as well as establish bounds for the…

Combinatorics · Mathematics 2025-06-27 William B. Kinnersley , Nikolas Townsend

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 investigate the game of cops and robber, played on a finite graph, between one cop and one robber. If the cop can force a win on a graph, the graph is called cop-win. We describe a procedure we call corner ranking, performed on a graph,…

Combinatorics · Mathematics 2017-03-14 David Offner , Kerry Ojakian

In the `Covering' pursuit game on a graph, a robber and a set of cops play alternately, with the cops each moving to an adjacent vertex (or not moving) and the robber moving to a vertex at distance at most 2 from his current vertex. The aim…

Combinatorics · Mathematics 2025-04-22 Benjamin Gillott

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

A generalization of hyperopic cops and robber, analogous to the $k$-visibility cops and robber, is introduced in this paper. For a positive integer $k$ the $k$-hyperopic game of cops and robber is defined similarly as the usual cops and…

Combinatorics · Mathematics 2024-10-24 Nicholas Crawford , Vesna Iršič Chenoweth

We study two-player security games which can be viewed as sequences of nonzero-sum matrix games played by an Attacker and a Defender. The evolution of the game is based on a stochastic fictitious play process. Players do not have access to…

Computer Science and Game Theory · Computer Science 2010-03-16 Kien C. Nguyen , Tansu Alpcan , Tamer Basar