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 minimum number of probes necessary per round to locate the robber on a given graph G is the localization number ζ(G). In this paper, we improve the bounds for dense random graphs determining the asymptotic behaviour of ζ(G). Moreover, we extend the argument to sparse graphs.
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