English
Related papers

Related papers: Locating a robber with multiple probes

200 papers

Various models to quantify the reliability of a network have been studied where certain components of the graph may fail at random and the probability that the remaining graph is connected is the proxy for reliability. In this work we…

Combinatorics · Mathematics 2020-11-24 Maimoonah Ahmed , Ben Cameron

Cops and Robber is a well-studied two-player pursuit-evasion game played on a graph, where a group of cops tries to capture the robber. The \emph{cop number} of a graph is the minimum number of cops required to capture the robber.…

Discrete Mathematics · Computer Science 2025-04-11 Sandip Das , Harmender Gahlawat

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 consider a surrounding variant of cops and robbers on graphs of bounded genus. We obtain bounds on the number of cops required to surround a robber on planar graphs, toroidal graphs, and outerplanar graphs. We also obtain improved bounds…

Combinatorics · Mathematics 2019-11-05 Peter Bradshaw , Seyyed Aliasghar Hosseini

We consider a variant of Cops and Robbers in which the robber may traverse as many edges as he likes in each turn, with the constraint that he cannot pass through any vertex occupied by a cop. We study this model on several classes of…

Combinatorics · Mathematics 2022-05-17 William B. Kinnersley , Nikolas Townsend

We consider the localization game played on graphs, wherein a set of cops attempt to determine the exact location of an invisible robber by exploiting distance probes. The corresponding optimization parameter for a graph $G$ is called the…

Combinatorics · Mathematics 2020-01-27 Anthony Bonato , William B. Kinnersley

The deduction game is a variation of the game of cops and robber on graphs in which searchers must capture an invisible evader in at most one move. Searchers know each others' initial locations, but can only communicate if they are on the…

Combinatorics · Mathematics 2024-12-24 Andrea Burgess , Danny Dyer , Mozhgan Farahani

We consider the localization game played on graphs in which a cop tries to determine the exact location of an invisible robber by exploiting distance probes. The corresponding graph parameter $\zeta(G)$ for a given graph $G$ is called the…

Combinatorics · Mathematics 2020-09-07 Andrzej Dudek , Sean English , Alan Frieze , Calum MacRury , Pawel Pralat

In this paper we study the concurrent cops and robber (CCCR) game. CCCR follows the same rules as the classical, turn-based game, except for the fact that the players move simultaneously. The cops' goal is to capture the robber and the…

Discrete Mathematics · Computer Science 2015-06-12 Georgios Konstantinidis , Athanasios Kehagias

In the game of cops and robber, the cops try to capture a robber moving 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 $G$. The biggest open conjecture in this area…

Combinatorics · Mathematics 2018-09-25 Pawel Pralat , Nicholas Wormald

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

In this paper we analyze a variant of the pursuit-evasion game on a graph $G$ where the intruder occupies a vertex, is allowed to move to adjacent vertices or remain in place, and is 'invisible' to the searcher, meaning that the searcher…

Combinatorics · Mathematics 2022-04-07 Anton Bernshteyn , Eugene Lee

We consider a variant of Cops and Robbers wherein each edge traversed by the robber is deleted from the graph. The focus is on determining the minimum number of cops needed to capture a robber on a graph $G$, called the {\em bridge-burning…

Combinatorics · Mathematics 2018-12-27 William B. Kinnersley , Eric Peterson

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

The game of Cops and Robber is traditionally played on a finite graph. The purpose of this paper is to introduce and analyse the game that is played on an arbitrary geodesic space (a compact, path-connected space endowed with intrinsic…

Metric Geometry · Mathematics 2026-01-14 Bojan Mohar

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 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

We investigate a pursuit-evasion game on an undirected graph in which a robber, moving at a fixed constant speed, attempts to evade a team of cops who are blind to the robber's location and can quickly travel between any pair of vertices in…

Combinatorics · Mathematics 2025-12-01 Hector Buffière , Rutger Campbell , Kevin Hendrey , Sang-il Oum

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

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
‹ Prev 1 3 4 5 6 7 10 Next ›