Related papers: The Cops & Robber game on series-parallel graphs

In this paper we analyze and model three open problems posed by Harris, Insko, Prieto-Langarica, Stoisavljevic, and Sullivan in 2020 concerning the tipsy cop and robber game on graphs. The three different scenarios we model account for…

We present an algorithm of time complexity $O(kn^{k+2})$ deciding whether a graph $G$ on $n$ vertices is $k$-copwin. The fastest algorithm thus far had time complexity $O(n^{2k+2})$.

Several variants of the cops and robbers (CR) game have been studied in the past. In this paper we examine a novel variant, which is played between two cops, each one independently trying to catch a "passive robber". We will call this the…

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…

We study zombies and survivor, a variant of the game of cops and robber on graphs. In this variant, the single survivor plays the role of the robber and attempts to escape from the zombies that play the role of the cops. The zombies are…

We consider a variant of Cops and Robbers in which the robber may traverse as many edges as he likes in each turn, with the constraint that he cannot pass through any vertex occupied by a cop. We study this model on several classes of…

A gambler moves on the vertices $1, \ldots, n$ of a graph using the probability distribution $p_{1}, \ldots, p_{n}$. A cop pursues the gambler on the graph, only being able to move between adjacent vertices. What is the expected number of…

The main topic of this paper is motivated by a localization problem in cellular networks. Given a graph $G$ we want to localize a walking agent by checking his distance to as few vertices as possible. The model we introduce is based on a…

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 present two efficient algorithms that compute the optimal strategy for cop in the game of Cop v.s. Gambler where the gambler's strategy is not optimal but known to the cop. The first algorithm is analogous to Bellman-Ford algorithm for…

We show that the cop number of every generalized Petersen graph is at most 4. The strategy is to play a modified game of cops and robbers on an infinite cyclic covering space where the objective is to capture the robber or force the robber…

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…

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…

We study the computational complexity of a perfect-information two-player game proposed by Aigner and Fromme. The game takes place on an undirected graph where n simultaneously moving cops attempt to capture a single robber, all moving at…

This paper is a contribution to the classical cops and robber problem on a graph, directed to two-dimensional grids and toroidal grids. These studies are generally aimed at determining the minimum number of cops needed to capture the robber…

We bound expected capture time and throttling number for the cop versus gambler game on a connected graph with $n$ vertices, a variant of the cop versus robber game that is played in darkness, where the adversary hops between vertices using…

We show that the cop number of any graph on 18 or fewer vertices is at most 3. This answers a question posed by Andreae in 1986, as well as more recently by Baird et al. We also find all 3-cop-win graphs on 11 vertices, narrow down 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 cop throttling number $th_c(G)$ of a graph $G$ for the game of Cops and Robbers is the minimum of $k + capt_k(G)$, where $k$ is the number of cops and $capt_k(G)$ is the minimum number of rounds needed for $k$ cops to capture the robber…

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…