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Related papers: The Robber Locating game

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We prove new theoretical results about several variations of the cop and robber game on graphs. First, we consider a variation of the cop and robber game which is more symmetric called the cop and killer game. We prove for all $c < 1$ that…

Discrete Mathematics · Computer Science 2017-11-01 Espen Slettnes , Carl Joshua Quines , Shen-Fu Tsai , Jesse Geneson

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

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

This paper considers a game in which a single cop and a single robber take turns moving along the edges of a given graph $G$. If there exists a strategy for the cop which enables it to be positioned at the same vertex as the robber…

Data Structures and Algorithms · Computer Science 2019-08-20 Thomas Erlebach , Jakob T. Spooner

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 study a variant of the classical cop-robber game played on compact metric graphs, where each edge is assigned a positive length and identified with a real interval of corresponding length. In this setting, both the cop and the robber…

Combinatorics · Mathematics 2025-12-23 Daniel Berend , Michael D. Boshernitzan

We consider "Containment": a variation of the graph pursuit game of Cops and Robber 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), and the…

Combinatorics · Mathematics 2019-03-19 Danny Crytser , Natasha Komarov , John Mackey

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

In the game of \emph{cops and robbers} on a graph $G = (V,E)$, $k$ cops try to catch a robber. On the cop turn, each cop may move to a neighboring vertex or remain in place. On the robber's turn, he moves similarly. The cops win if there is…

Combinatorics · Mathematics 2012-04-03 Andrew Beveridge , Paolo Codenotti , Aaron Maurer , John McCauley , Silviya Valeva

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 show that the expected time for a smart "cop" to catch a drunk "robber" on an $n$-vertex graph is at most $n + {\rm o}(n)$. More precisely, let $G$ be a simple, connected, undirected graph with distinguished points $u$ and $v$ among its…

Combinatorics · Mathematics 2014-11-05 Natasha Komarov , Peter Winkler

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…

We discuss winning possibilities of players in various variants of cops and robber game played on large random graphs, a testbed for various kinds of network queries, search problems in particular. We explore the use of logic frameworks to…

Logic in Computer Science · Computer Science 2025-12-01 Sourav Chakraborty , Sujata Ghosh , Smiha Samanta

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

The main topic of this paper is motivated by a localization problem in cellular networks. Given a graph $G$ we want to localize a walking agent by checking his distance to as few vertices as possible. The model we introduce is based on a…

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 study a game of pursuit and evasion introduced by Seager in 2012, in which a cop searches the robber from outside the graph, using distance queries. A graph on which the cop wins is called locatable. In her original paper, Seager asked…

Combinatorics · Mathematics 2014-02-13 Richard A. B. Johnson , Sebastian Koch

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

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

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…