Related papers: Cops and Robber Game with a Fast Robber on Expande…
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…
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…
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…
Motivated by a biological scenario illustrated in the YouTube video \url{ https://www.youtube.com/watch?v=Z_mXDvZQ6dU} where a neutrophil chases a bacteria cell moving in random directions, we present a variant of the cop and robber game on…
In this note, we prove that all cop-win graphs G in the game in which the robber and the cop move at different speeds s and s' with s'<s, are \delta-hyperbolic with \delta=O(s^2). We also show that the dependency between \delta and s is…
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,…
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…
We consider the Cops and Robbers game played on finite simple graphs. In a graph $G$, the number of cops required to capture a robber in the Cops and Robbers game is denoted by $c(G)$. For all graphs $G$, $c(G) \leq \alpha(G) \leq…
We introduce two variations of the cops and robber game on graphs. These games yield two invariants in $\mathbb{Z}_+\cup\{\infty\}$ for any connected graph $\Gamma$, the {weak cop number $\mathsf{wcop}(\Gamma)$} and the {strong cop number…
In the classic cop and robber game, two players--the cop and the robber--take turns moving to a neighboring vertex or staying at their current position. The cop aims to capture the robber, while the robber tries to evade capture. A graph…
We provide a sublinear bound on the cop throttling number of a connected graph. Related to the graph searching game Cops and Robbers, the cop throttling number, written $\mathrm{th}_c(G)$, is given by…
The 'Cheating Robot' version of Cops and Robbers is played on a finite, simple, connected graph. The players move in the same time period. However, before moving, the robot observes to which vertices the cops are moving and it is fast…
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…
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…
The game of cops and robbers, played on a fixed graph $G$, is a two-player game, where the cop and the robber (the players) take turns in moving to adjacent vertices. The game finishes if the cop lands on the robber's vertex. In that case…
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…
In the cops and robber games played on a simple graph $G$, Aigner and Fromme's lemma states that one cop can guard a shortest path in the sense that the robber cannot enter this path without getting caught after finitely many steps. In this…
We survey results at the intersection of topological graph theory and the game of Cops and Robbers, focusing on results, conjectures, and open problems for the cop number of a graph embedded on a surface. After a discussion on results for…
The game of Cops and Robber is traditionally played on a finite graph. The purpose of this note is to introduce and analyze the game that is played on an arbitrary geodesic space. The game is defined in such a way that it preserves the…
We investigate extremal graphs related to the game of Cops and Robbers. We focus on graphs where a single cop can catch the robber; such graphs are called cop-win. The capture time of a cop-win graph is the minimum number of moves the cop…