Localization game for random geometric graphs

The localization game is a two player combinatorial played on graph G=(V,E). cops choose set of vertices S1⊆V with |S1|=k. robber then chooses vertex v∈V whose location hidden from the cops, but learn distance between current position and in S1. If this information sufficient to locate robber, win immediately; otherwise another S2⊆V |S2|=k, may move neighboring vertex. new distances are presented, if can deduce based all they accumulated thus far, win; otherwise, round begins. has strategy avoid being captured, she wins. number defined be smallest integer k so that game. In paper we determine (up poly-logarithmic factors) random geometric G∈G(n,r) slightly above connectivity threshold.