Localization Game for Random Graphs

Andrzej Dudek, Sean English, Alan Frieze, Calum MacRury, Pawel Pralat

Published 2019-10-24Version 1

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.