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Very sharp transitions in one-dimensional MANETs
(2005)
We investigate how quickly phase transitions can occur in one-dimensional geometric random graph models of MANETs. In the case of graph connectivity, we show that the transition width behaves like 1/n (when the number n ...
On zero-one laws for connectivity in one-dimensional geometric random graphs
(2006)
We consider the geometric random graph where n points are distributed uniformly and independently on the unit interval [0,1]. Using the method of first and second moments, we provide a simple proof of the "zero-one" law ...