相关论文: Cops and robbers on oriented toroidal grids

This paper considers a game in which a single cop and a single robber take turns moving along the edges of a given graph $G$. If there exists a strategy for the cop which enables it to be positioned at the same vertex as the robber…

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 consider the game of Cops and Robber played on the Cartesian product of two trees. Assuming the players play perfectly, it is shown that if there are two cops in the game, then the length of the game (known as the 2-capture time of the…

The game of cops and robber is a two-player turn-based game played on a graph where the cops try to capture the robber. The cop number of a graph $G$, denoted by $c(G)$ is the minimum number of cops required to capture the robber. For a…

The cop throttling number of a graph, introduced in 2018 by Breen et al., optimizes the balance between the number of cops used and the number of rounds required to catch the robber in a game of Cops and Robbers. In 2019, Cox and Sanaei…

A relational characterization of cop-win graphs was provided by Nowakowski and Winkler in their seminal paper on the game of Cops and Robbers. As a by-product of that characterization, each cop-win graph is assigned a unique ordinal, which…

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…

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…

We study the problem of cops and robbers on the grid where the robber is allowed to move faster than the cops. It is well known that two cops are necessary and sufficient to catch the robber on any finite grid when the robber has unit…

We consider a Cops-and-Robber game played on the subsets of an $n$-set. The robber starts at the full set; the cops start at the empty set. On each turn, the robber moves down one level by discarding an element, and each cop moves up one…

This paper describes a 720-vertex connected planar graph G such that cop1(G), denoting the minimum number of cops needed to catch the robber in the 1-cop-move game on G, is at least 4 and at most 7. Furthermore, G has a connected subgraph H…

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 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…

Mohar recently adapted the classical game of Cops and Robber from graphs to metric spaces, thereby unifying previously studied pursuit-evasion games. He conjectured that finitely many cops can win on any compact geodesic metric space, and…

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 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…

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…

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…

The cops-and-robber (CR) game has been used in mobile robotics as a discretized model (played on a graph G) of pursuit/evasion problems. The "classic" CR version is a perfect information game: the cops' (pursuer's) location is always known…