2021
DOI: 10.48550/arxiv.2102.10352
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Localization Game for Random Geometric Graphs

Abstract: The localization game is a two player combinatorial game played on a graph G = (V, E). The cops choose a set of vertices S 1 ⊆ V with |S 1 | = k. The robber then chooses a vertex v ∈ V whose location is hidden from the cops, but the cops learn the graph distance between the current position of the robber and the vertices in S 1 . If this information is sufficient to locate the robber, the cops win immediately; otherwise the cops choose another set of vertices S 2 ⊆ V with |S 2 | = k, and the robber may move to… Show more

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“…The bounds for dense graphs were consecutively improved in [19], and the arguments were extended to sparse graphs. The localization game was also recently studied for random geometric graphs [30]. We direct the reader to the book [7] for more graph searching games in the context of random graphs.…”
Section: Related Workmentioning
confidence: 99%
“…The bounds for dense graphs were consecutively improved in [19], and the arguments were extended to sparse graphs. The localization game was also recently studied for random geometric graphs [30]. We direct the reader to the book [7] for more graph searching games in the context of random graphs.…”
Section: Related Workmentioning
confidence: 99%