Two-point concentration in random geometric graphs

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Two-point concentration in random geometric graphs
A random geometric graph Gn is constructed by taking vertices X1, . . . , Xn Rd at random (i.i.d. according to some probability distribution with a bounded density function) and including an edge between Xi and Xj if Xi -Xj < r where r = r(n) > 0. We prove a conjecture of Penrose ([14]) stating that when r = r(n) is chosen such that nrd = o(ln n) then the probability distribution of the clique number (Gn) becomes concentrated on two consecutive integers and we show that the same holds for a number of other graph parameters including the chromatic number (Gn).
Tobias Müller
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2008
Authors Tobias Müller
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