Related papers: An anti-incursion algorithm for unknown probabilis…
The optimal control of a "blind" pursuer searching for an evader moving on a road network and heading at a known speed toward a set of goal vertices is considered. To aid the "blind" pursuer, certain roads in the network have been…
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…
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 this paper, we develop efficient exact and approximate algorithms for computing a maximum independent set in random graphs. In a random graph $G$, each pair of vertices are joined by an edge with a probability $p$, where $p$ is a…
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…
For any given vertices $u$ and $v$ in a graph, the hitting time of a random walk on a finite graph is the number of steps it takes for a random walk to reach vertex $v$ starting at vertex $u$. The expected value of the hitting time is the…
We investigate a cheating robot version of Cops and Robber, first introduced by Huggan and Nowakowski, where both the cops and the robber move simultaneously, but the robber is allowed to react to the cops' moves. For conciseness, we refer…
Given a connected graph $G$ with some subset of its vertices excited and a fixed target vertex, in the geodesic-biased random walk on $G$, a random walker moves as follows: from an unexcited vertex, she moves to a uniformly random…
A cat and mouse play a pursuit and evasion game on a connected graph $G$ with $n$ vertices. The mouse moves to vertices $m_1,m_2,\dots$ of $G$ where $m_i$ is in the closed neighbourhood of $m_{i-1}$ for $i\geq2$. The cat tests vertices…
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…
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…
Cops and Robbers games have been studied for the last few decades in computer science and mathematics. As in general pursuit evasion games, pursuers (cops) seek to capture evaders (robbers); however, players move in turn and are constrained…
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 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 investigate the game of cops and robber, played on a finite graph, between one cop and one robber. If the cop can force a win on a graph, the graph is called cop-win. We describe a procedure we call corner ranking, performed on a graph,…
Cops and Robber is a family of two-player games played on graphs in which one player controls a number of cops and the other player controls a robber. In alternating turns, each player moves (all) their figures. The cops try to capture the…
In this paper, we study the game of cops and robber on the class of graphs with no even hole (induced cycle of even length) and claw (a star with three leaves). The cop number of a graph $G$ is defined as the minimum number of cops needed…
We study the escape probability problem in random walks over graphs. Given vertices, $s,t,$ and $p$, the problem asks for the probability that a random walk starting at $s$ will hit $t$ before hitting $p$. Such probabilities can be…
In the classic cop and robber game, two players--the cop and the robber--take turns moving to a neighboring vertex or staying at their current position. The cop aims to capture the robber, while the robber tries to evade capture. A graph…
The game of Cops and Robbers on graphs is a well-studied pursuit--evasion model whose central parameter, the cop number, captures the minimum number of pursuers required to guarantee capture of an adversary on a given graph. While the cop…