Localization Game for Random Graphs

Abstract

We consider the localization game played on graphs in which a cop tries to determine the exact location of an invisible robber by exploiting distance probes. The corresponding graph parameter $\zeta (G)$ for a given graph $G$ is called the localization number. In this paper, we improve the bounds for dense random graphs determining an asymptotic behaviour of $\zeta (G)$. Moreover, we extend the argument to sparse graphs.