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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…

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 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 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

We study pursuit-evasion in a polygonal environment with polygonal obstacles. In this turn based game, an evader $e$ is chased by pursuers $p_1, p_2, ..., p_{\ell}$. The players have full information about the environment and the location…

Computational Geometry · Computer Science 2014-10-21 Brendan Ames , Andrew Beveridge , Rosalie Carlson , Claire Djang , Volkan Isler , Stephen Ragain , Maxray Savage

\textsc{Cops and Robber} is a game played on graphs where a set of \textit{cops} aim to \textit{capture} the position of a single \textit{robber}. The main parameter of interest in this game is the \textit{cop number}, which is the minimum…

Combinatorics · Mathematics 2025-12-29 Harmender Gahlawat

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

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 pursuit-evasion differential game with finite number of pursuers and one evader in Hilbert space with geometric constraints on the control functions of players. We solve the game by presenting explicit strategies for pursuers…

Optimization and Control · Mathematics 2015-06-03 Mehdi Salimi , Massimiliano Ferrara

This paper investigates obstacle-free simple motion pursuit-evasion problems where the pursuer is faster and game termination is point capture. It is well known that the interior of the Apollonius Circle (AC) is the evader's dominance…

Optimization and Control · Mathematics 2022-03-24 Michael Dorothy , Dipankar Maity , Daigo Shishika , Alexander Von Moll

We propose a decentralized solution for a pursuit-evasion game involving a heterogeneous group of rational (selfish) pursuers and a single evader based on the framework of potential games. In the proposed game, the evader aims to delay (or,…

Systems and Control · Electrical Eng. & Systems 2021-08-19 Yoonjae Lee , Efstathios Bakolas

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 introduce and study a new search-type problem with ($n+1$)-robots on a disk. The searchers (robots) all start from the center of the disk, have unit speed, and can communicate wirelessly. The goal is for a distinguished robot (the queen)…

Discrete Mathematics · Computer Science 2018-05-10 J. Czyzowicz , K. Georgiou , R. Killick , E. Kranakis , D. Krizanc , L. Narayanan , J. Opatrny , S. Shende

We consider a pursuit-evasion game that describes the process of extinguishing a fire burning on the nodes of an undirected graph. We denote the minimum number of firefighters required by ffn(G) and provide almost sharp bounds to this graph…

Computational Complexity · Computer Science 2026-04-15 Julius Althoetmar , Jamico Schade , Torben Schürenberg

We study the entanglement game, which is a version of cops and robbers, on sparse graphs. While the minimum degree of a graph G is a lower bound for the number of cops needed to catch a robber in G, we show that the required number of cops…

Discrete Mathematics · Computer Science 2018-01-23 Anders Martinsson , Florian Meier , Patrick Schnider , Angelika Steger

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

Given a two-dimensional polygonal space, the multi-robot visibility-based pursuit-evasion problem tasks several pursuer robots with the goal of establishing visibility with an arbitrarily fast evader. The best known complete algorithm for…

Robotics · Computer Science 2021-04-12 Trevor Olsen , Anne M. Tumlin , Nicholas M. Stiffler , Jason M. O'Kane

Graph Exploration problems ask a searcher to explore an unknown environment. The environment is modeled as a graph, where the searcher needs to visit each vertex beginning at some vertex. Treasure Hunt problems are a variation of Graph…

Computational Complexity · Computer Science 2024-12-02 Janosch Fuchs , Christoph Grüne , Tom Janßen

We study the m-eternal domination problem from the perspective of the attacker. For many graph classes, the minimum required number of guards to defend eternally is known. By definition, if the defender has less than the required number of…

Discrete Mathematics · Computer Science 2022-04-07 Václav Blažej , Jan Matyáš Křišťan , Tomáš Valla

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