Chasing robbers on percolated random geometric graphs
DOI:
https://doi.org/10.55016/ojs/cdm.v10i1.62293Abstract
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 $G$ is called the cop number of $G$. We focus on $\G(n,r,p)$, a percolated random geometric graph in which $n$ vertices are chosen uniformly at random and independently from $[0,1]^2$, and two vertices are adjacent with probability $p$ if the Euclidean distance between them is at most $r$. We present asymptotic results for the game of Cops and Robber played on $\G(n,r,p)$ for a wide range of $p=p(n)$ and $r=r(n)$.Downloads
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