The acquaintance time of (percolated) random geometric graphs
نویسندگان
چکیده
منابع مشابه
The acquaintance time of (percolated) random geometric graphs
In this paper, we study the acquaintance time AC(G) defined for a connected graph G. We focus on G(n, r, p), a random subgraph of a random geometric graph in which n vertices are chosen uniformly at random and independently from [0, 1], and two vertices are adjacent with probability p if the Euclidean distance between them is at most r. We present asymptotic results for the acquaintance time of...
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In this short note, we prove a conjecture of Benjamini, Shinkar, and Tsur on the acquaintance time AC(G) of a random graph G ∈ G(n, p). It is shown that asymptotically almost surely AC(G) = O(log n/p) for G ∈ G(n, p), provided that pn−log n−log log n→∞ (that is, above the threshold for Hamiltonicity). Moreover, we show a matching lower bound for dense random graphs, which also implies that asym...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2015
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2015.02.021