High-dimensional random geometric graphs and their clique number
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چکیده
We study the behavior of random geometric graphs in high dimensions. We show that as the dimension grows, the graph becomes similar to an Erdős-Rényi random graph. We pay particular attention to the clique number of such graphs and show that it is very close to that of the corresponding Erdős-Rényi graph when the dimension is larger than log n where n is the number of vertices. The problem is motivated by a statistical problem of testing dependencies..
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تاریخ انتشار 2010