Related papers: Capturing the Drunk Robber on a Graph
We study a variation of the classical pursuit-evasion game of Cops and Robbers in which agents are required to move to an adjacent vertex on every turn. We explore how the minimum number of cops needed to catch the robber can change when…
We consider a cops and robber game where the cops are blocking edges of a graph, while the robber occupies its vertices. At each round of the game, the cops choose some set of edges to block and right after the robber is obliged to move to…
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…
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 a well known pursuit-evasion game played on graphs. It has been proved \cite{bounded_degree} that cubic graphs can have arbitrarily large cop number $c(G)$, but the known constructions show only that the set…
A hole in a graph is an induced cycle of length at least 4. We give a simple winning strategy for t-3 cops to capture a robber in the game of cops and robbers played in a graph that does not contain a hole of length at least t. This…
Cops and Robbers is a pursuit-evasion game played on graphs, of which many variants have been developed and studied. We introduce a variant of this game, "Sneaky-Active Cops and Robbers", where all cops and robber must move on their turn,…
We consider a class of pursuit-evasion problems where an evader enters a directed acyclic graph and attempts to reach one of the terminal nodes. A pursuer enters the graph at a later time and attempts to capture the evader before it reaches…
A cop tries to capture a robber in a topological space $X$ being unable to see him. For which spaces $X$ does the cop have a strategy which allows him to capture the robber independently of his efforts to escape? In other words, when is…
We adapt the Gy\'{a}rf\'{a}s path argument to prove that $t-2$ cops can capture a robber, in at most $t-1$ moves, in the game of cops and robbers played in a graph that does not contain the $t$-vertex path as an induced subgraph.
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…
The cop number of a graph $G$ is the smallest $k$ such that $k$ cops win the game of cops and robber on $G$. We investigate the maximum cop number of geometric intersection graphs, which are graphs whose vertices are represented by…
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…
In many variants of the game of Cops and Robbers on graphs, multiple cops play against a single robber. In 2019, Cox and Sanaei introduced a variant of the game that gives the robber a more active role than simply evading the cop. In their…
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…
\textit{Pursuit-evasion games} have been intensively studied for several decades due to their numerous applications in artificial intelligence, robot motion planning, database theory, distributed computing, and algorithmic theory.…
The cover time of a finite connected graph is the expected number of steps needed for a simple random walk on the graph to visit all vertices of the graph. It is known that the cover time of any finite connected $n$-vertex graph is at least…
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…
This paper analyzes the meeting time between a pair of pursuer and evader performing random walks on digraphs. The existing bounds on the meeting time usually work only for certain classes of walks and cannot be used to formulate…
A \emph{periodic graph} ${\cal G}=(G_0, G_1, G_2, \dots)$ with period $p$ is an infinite periodic sequence of graphs $G_i = G_{i + p} = (V,E_i)$, where $i \geq 0$. The graph $G=(V,\cup_i E_i)$ is called the footprint of ${\cal G}$.…