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arXiv · 1712.03311

A note on the localization number of random graphs: diameter two case

Andrzej Dudek·Alan Frieze·Wesley Pegden
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Abstract

We study the localization game on dense random graphs. In this game, a {\em cop} $x$ tries to locate a {\em robber} $y$ by asking for the graph distance of $y$ from every vertex in a sequence of sets $W_1,W_2,\ldots,W_\ell$. We prove high probability upper and lower bounds for the minimum size of each $W_i$ that will guarantee that $x$ will be able to locate $y$.

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Andrzej Dudek, Alan Frieze, Wesley Pegden. 2019-05-14. A note on the localization number of random graphs: diameter two case. https://arxiv.org/abs/1712.03311

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