3 research outputs found
Chasing robbers on percolated random geometric graphs
In this paper, we study the vertex pursuit game of \emph{Cops and Robbers}, in which cops try to capture a robber on the vertices of a graph. The minimum number of cops required to win on a given graph is called the cop number of . We focus on \G(n,r,p), a percolated random geometric graph in which vertices are chosen uniformly at random and independently from , and two vertices are adjacent with probability if the Euclidean distance between them is at most . We present asymptotic results for the game of Cops and Robber played on \G(n,r,p) for a wide range of and
Chasing robbers on percolated random geometric graphs
In this paper, we study the vertex pursuit game of \emph{Cops and Robbers}, in which cops try to capture a robber on the vertices of a graph. The minimum number of cops required to win on a given graph is called the cop number of . We focus on \G(n,r,p), a percolated random geometric graph in which vertices are chosen uniformly at random and independently from , and two vertices are adjacent with probability if the Euclidean distance between them is at most . We present asymptotic results for the game of Cops and Robber played on \G(n,r,p) for a wide range of and
Chasing robbers on percolated random geometric graphs
In this paper, we study the vertex pursuit game of \emph{Cops and Robbers}, in which cops try to capture a robber on the vertices of a graph. The minimum number of cops required to win on a given graph is called the cop number of . We focus on \G(n,r,p), a percolated random geometric graph in which vertices are chosen uniformly at random and independently from , and two vertices are adjacent with probability if the Euclidean distance between them is at most . We present asymptotic results for the game of Cops and Robber played on \G(n,r,p) for a wide range of and