Related papers: An anti-incursion algorithm for unknown probabilis…
We consider a game in which a cop searches for a moving robber on a graph using distance probes, studied by Carragher, Choi, Delcourt, Erickson and West, which is a slight variation on one introduced by Seager. Carragher, Choi, Delcourt,…
In the game of Cops and Robbers, the capture time of a graph is the minimum number of moves needed by the cops to capture the robber, assuming optimal play. We prove that the capture time of the $n$-dimensional hypercube is $\Theta (n\ln…
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.…
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…
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…
We consider the new game of Cops and Attacking Robbers, which is identical to the usual Cops and Robbers game except that if the robber moves to a vertex containing a single cop, then that cop is removed from the game. We study the minimum…
The game of Cops and Robbers is a well known game played on graphs. In this paper we consider the class of graphs of bounded diameter. We improve the strategy of cops and previously used probabilistic method which results in an improved…
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…
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…
We introduce the game of Surrounding Cops and Robbers on a graph, as a variant of the original game of Cops and Robbers. In contrast to the original game in which the cops win by occupying the same vertex as the robber, they now win by…
We consider the cop-throttling number of a graph $G$ for the game of Cops and Robbers, which is defined to be the minimum of $(k + \text{capt}_k(G))$, where $k$ is the number of cops and $\text{capt}_k(G)$ is the minimum number of rounds…
The game of cops and robbers is played on a fixed (finite or infinite) graph $G$. The cop chooses his starting position, then the robber chooses his. After that, they take turns and move to adjacent vertices, or stay at their current…
We investigate a cops and robber game on directed graphs, where the robber moves along the arcs of the graph, while the cops can select any position at each time step. Our main focus is on the cop number: the minimum number of cops required…
We study a simple random process in which vertices of a connected graph reach consensus through pairwise interactions. We compute outcome probabilities, which do not depend on the graph structure, and consider the expected time until a…
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 "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…
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…
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…
The Cops and Robber game is played on undirected finite graphs. $k$ cops and one robber are positioned on vertices and take turn in moving along edges. The cops win if, after a move, a cop and the robber are on the same vertex. A graph is…
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…