Related papers: Guarding isometric subgraphs and Cops and Robber i…
We consider a variant of the Cops and Robber game, 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 occupied by a cop. Let c_{infty}(G) denote the…
We study the zero-visibility cops and robbers game, where the robber is invisible to the cops until they are caught. This differs from the classic game where full information about the robber's location is known at any time. A previously…
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…
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…
We consider a game in which a cop searches for a moving robber on a connected graph using distance probes, which is a slight variation on one introduced by Seager. Carragher, Choi, Delcourt, Erickson and West showed that for any $n$-vertex…
In the ordinary version of the pursuit-evasion game "cops and robbers", a team of cops and a robber occupy vertices of a graph and alternately move along the graph's edges, with perfect information about each other. If a cop lands on the…
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…
The game of \emph{Cops and Robber} is usually played on a graph, where a group of cops attempt to catch a robber moving along the edges of the graph. The \emph{cop number} of a graph is the minimum number of cops required to win the game.…
In the cops and robber game, there are multiple cops and a single robber taking turns moving along the edges of a graph. The goal of the cops is to capture the robber (move to the same vertex as the robber) and the goal of the robber is to…
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…
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…
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…
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…
The game of cops and robber is a turn based vertex pursuit game played on a connected graph between a team of cops and a single robber. The cops and the robber move alternately along the edges of the graph. We say the team of cops win the…
Here we merge the two fields of Cops and Robbers and Graph Pebbling to introduce the new topic of Cops and Robbers Pebbling. Both paradigms can be described by moving tokens (the cops) along the edges of a graph to capture a special token…
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…
We consider the effect on the length of the game of Cops and Robbers when more cops are added to the game play. In Overprescribed Cops and Robbers, as more cops are added, the capture time (the minimum length of the game assuming optimal…
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…
Cops and robbers is a pursuit-evasion game played on graphs. We completely classify the cop numbers for $n \times n$ knight graphs and queen graphs. This completes the classification of the cop numbers for all $n \times n$ classical chess…
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…