Abstract
We consider the Eschenauer-Gligor key predistribution scheme under the condition of partial visibility with i.i.d. on-off links between pairs of nodes. This situation is modeled as the intersection of two random graphs, namely a random key graph and an Erdős-Rényi (ER) graph. For this class of composite random graphs we give various improvements on a recent result by Yağan [IEEE Transactions on Information Theory, 58(6):3821-3835, 2012] concerning zero-one laws for the absence of isolated nodes.
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